Memoirs of the American Mathematical Society最新文献

{"title":"Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori","authors":"Steven Boyer, Cameron McA. Gordon, Xingru Zhang","doi":"10.1090/memo/1469","DOIUrl":"https://doi.org/10.1090/memo/1469","url":null,"abstract":"<p>We show that if a hyperbolic knot manifold <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\">\u0000 <mml:semantics>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">M</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> contains an essential twice-punctured torus <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\">\u0000 <mml:semantics>\u0000 <mml:mi>F</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">F</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> with boundary slope <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"beta\">\u0000 <mml:semantics>\u0000 <mml:mi>β<!-- β --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">beta</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and admits a filling with slope <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"alpha\">\u0000 <mml:semantics>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">alpha</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> producing a Seifert fibred space, then the distance between the slopes <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"alpha\">\u0000 <mml:semantics>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">alpha</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"beta\">\u0000 <mml:semantics>\u0000 <mml:mi>β<!-- β --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">beta</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is less than or equal to <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"5\">\u0000 <mml:semantics>\u0000 <mml:mn>5</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">5</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> unless <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\">\u0000 <mml:semantics>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">M</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is the exterior of the figure eight knot. The result is sharp; the bound of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"5\">\u0000 <mml:semantics>\u0000 <mml:mn>5</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">5</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> can be realized on infinitely many hyperbolic knot manifolds. We also determine distance bounds in the case that the fundamental group of the","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141216037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subgroup Decomposition in 𝖮𝗎𝗍(𝖥_{𝗇})","authors":"M. Handel, L. Mosher","doi":"10.1090/memo/1280","DOIUrl":"https://doi.org/10.1090/memo/1280","url":null,"abstract":"","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48171650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Propagating Terraces and the Dynamics of\u0000 Front-Like Solutions of Reaction-Diffusion Equations\u0000 on ℝ","authors":"P. Polácik","doi":"10.1090/memo/1278","DOIUrl":"https://doi.org/10.1090/memo/1278","url":null,"abstract":"We consider semilinear parabolic equations of the form ut = uxx + f(u), x ∈ R, t > 0, where f a C1 function. Assuming that 0 and γ > 0 are constant steady states, we investigate the large-time behavior of the front-like solutions, that is, solutions u whose initial values u(x, 0) are near γ for x ≈ −∞ and near 0 for x ≈ ∞. If the steady states 0 and γ are both stable, our main theorem shows that at large times, the graph of u(·, t) is arbitrarily close to a propagating terrace (a system of stacked traveling fonts). We prove this result without requiring monotonicity of u(·, 0) or the nondegeneracy of zeros of f . The case when one or both of the steady states 0, γ is unstable is considered as well. As a corollary to our theorems, we show that all front-like solutions are quasiconvergent: their ω-limit sets with respect to the locally uniform convergence consist of steady states. In our proofs we employ phase plane analysis, intersection comparison (or, zero number) arguments, and a geometric method involving the spatial trajectories {(u(x, t), ux(x, t)) : x ∈ R}, t > 0, of the solutions in question.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47138547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spiral Waves: Linear and Nonlinear Theory","authors":"Bjorn Sandstede, A. Scheel","doi":"10.1090/memo/1413","DOIUrl":"https://doi.org/10.1090/memo/1413","url":null,"abstract":"Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather than studying existence in a specific equation, we study properties of spiral waves in general reaction-diffusion systems. We show that many features of spiral waves are robust and to some extent independent of the specific model analyzed. To accomplish this, we present a suitable analytic framework, spatial radial dynamics, that allows us to rigorously characterize features such as the shape of spiral waves and their eigenfunctions, properties of the linearization, and finite-size effects. We believe that our framework can also be used to study spiral waves further and help analyze bifurcations, as well as provide guidance and predictions for experiments and numerical simulations. From a technical point of view, we introduce non-standard function spaces for the well-posedness of the existence problem which allow us to understand properties of spiral waves using dynamical systems techniques, in particular exponential dichotomies. Using these pointwise methods, we are able to bring tools from the analysis of one-dimensional coherent structures such as fronts and pulses to bear on these inherently two-dimensional defects.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45564385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Decorated Dyck paths, polyominoes, and the Delta conjecture","authors":"Michele D'Adderio, Alessandro Iraci, A. V. Wyngaerd","doi":"10.1090/memo/1370","DOIUrl":"https://doi.org/10.1090/memo/1370","url":null,"abstract":"<p>We discuss the combinatorics of decorated Dyck paths and decorated parallelogram polyominoes, extending to the decorated case the main results of both Haglund (“A proof of the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q comma t\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">q,t</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Schröder conjecture”, 2004) and Aval et al. (“Statistics on parallelogram polyominoes and a <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q comma t\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">q,t</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-analogue of the Narayana numbers”, 2014). This settles in particular the cases <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mathematical left-angle dot comma e Subscript n minus d Baseline h Subscript d Baseline mathematical right-angle\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">⟨<!-- ⟨ --></mml:mo>\u0000 <mml:mo>⋅<!-- ⋅ --></mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>e</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mi>d</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:msub>\u0000 <mml:mi>h</mml:mi>\u0000 <mml:mi>d</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">⟩<!-- ⟩ --></mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">langle cdot ,e_{n-d}h_drangle</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mathematical left-angle dot comma h Subscript n minus d Baseline h Subscript d Baseline mathematical right-angle\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">⟨<!-- ⟨ --></mml:mo>\u0000 <mml:mo>⋅<!-- ⋅ --></mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>h</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mi>d</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:msub>\u0000 <mml:mi>h</mml:mi>\u0000 <mml:mi>d</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">⟩<!-- ⟩ --></mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">langle cdot ,h_{n-d}h_drangle</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of the Delta conjecture of Haglund, Remmel and Wilson (“The delta conjec","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49011543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Congruence Lattices of Ideals in Categories and (Partial) Semigroups","authors":"J. East, N. Ruškuc","doi":"10.1090/memo/1408","DOIUrl":"https://doi.org/10.1090/memo/1408","url":null,"abstract":"This monograph presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative process of stacking certain normal subgroup lattices on top of each other to successively build congruence lattices of a chain of ideals. This is applied to several specific categories of: transformations; order/orientation preserving/reversing transformations; partitions; planar/annular partitions; Brauer, Temperley–Lieb and Jones partitions; linear and projective linear transformations; and partial braids. Special considerations are needed for certain small ideals, and technically more intricate theoretical underpinnings for the linear and partial braid categories.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44460644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Triangle-Free Process and the Ramsey\u0000 Number 𝑅(3,𝑘)","authors":"Gonzalo Fiz Pontiveros, Simon Griffiths, R. Morris","doi":"10.1090/memo/1274","DOIUrl":"https://doi.org/10.1090/memo/1274","url":null,"abstract":"","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60559038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Euclidean Structures and Operator Theory in Banach Spaces","authors":"N. Kalton, E. Lorist, L. Weis","doi":"10.1090/memo/1433","DOIUrl":"https://doi.org/10.1090/memo/1433","url":null,"abstract":"<p>We present a general method to extend results on Hilbert space operators to the Banach space setting by representing certain sets of Banach space operators <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma\">\u0000 <mml:semantics>\u0000 <mml:mi mathvariant=\"normal\">Γ<!-- Γ --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">Gamma</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> on a Hilbert space. Our assumption on <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma\">\u0000 <mml:semantics>\u0000 <mml:mi mathvariant=\"normal\">Γ<!-- Γ --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">Gamma</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is expressed in terms of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"alpha\">\u0000 <mml:semantics>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">alpha</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-boundedness for a Euclidean structure <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"alpha\">\u0000 <mml:semantics>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">alpha</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> on the underlying Banach space <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. This notion is originally motivated by <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper R\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">R</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {R}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>- or <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"gamma\">\u0000 <mml:semantics>\u0000 <mml:mi>γ<!-- γ --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">gamma</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-boundedness of sets of operators, but for example any operator ideal from the Euclidean space <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script l Subscript n Superscript 2\">\u0000 <mml:semantics>\u0000 <mml:msubsup>\u0000 <mml:mi>ℓ<!-- ℓ --></mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msubsup>\u0000 <mml:annotation encoding=\"application/x-tex\">ell ^2_n</mml:annotation>\u0000 </mml:sema","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45838940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters","authors":"G. K. Duong, N. Nouaili, H. Zaag","doi":"10.1090/memo/1411","DOIUrl":"https://doi.org/10.1090/memo/1411","url":null,"abstract":"We construct a solution for the Complex Ginzburg-Landau (CGL) equation in a general critical case, which blows up in finite time \u0000\u0000 \u0000 T\u0000 T\u0000 \u0000\u0000 only at one blow-up point. We also give a sharp description of its profile. In the first part, we formally construct a blow-up solution. In the second part we give the rigorous proof. The proof relies on the reduction of the problem to a finite dimensional one, and the use of index theory to conclude. The interpretation of the parameters of the finite dimension problem in terms of the blow-up point and time allows to prove the stability of the constructed solution. We would like to mention that the asymptotic profile of our solution is different from previously known profiles for CGL or for the semilinear heat equation.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43473916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster","authors":"Alexander Bors, Michael Giudici, C. Praeger","doi":"10.1090/memo/1427","DOIUrl":"https://doi.org/10.1090/memo/1427","url":null,"abstract":"<p>For a finite group <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, we denote by <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"omega left-parenthesis upper G right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>ω<!-- ω --></mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">omega (G)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> the number of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A u t left-parenthesis upper G right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>A</mml:mi>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Aut(G)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-orbits on <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, and by <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"o left-parenthesis upper G right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>o</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">o(G)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> the number of distinct element orders in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. In this paper, we are primarily concerned with the two quantities <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German d left-parenthesis upper G right-parenthesis colon-equal omega left-parenthesis upper G right-parenthesis minus o left-parenthesis upper G right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"fraktur\">d</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 ","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2019-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47590446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}