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The prime graphs of groups with arithmetically small composition factors 具有算术上小的组成因子的群的素数图
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-11-26 DOI: 10.1007/s10231-023-01388-x
Timothy J. Edwards, Thomas Michael Keller, Ryan M. Pesak, Karthik Sellakumaran Latha
{"title":"The prime graphs of groups with arithmetically small composition factors","authors":"Timothy J. Edwards, Thomas Michael Keller, Ryan M. Pesak, Karthik Sellakumaran Latha","doi":"10.1007/s10231-023-01388-x","DOIUrl":"https://doi.org/10.1007/s10231-023-01388-x","url":null,"abstract":"<p>We continue the study of prime graphs of finite groups, also known as Gruenberg–Kegel graphs. The vertices of the prime graph of a finite group are the prime divisors of the group order, and two vertices <i>p</i> and <i>q</i> are connected by an edge if and only if there is an element of order <i>pq</i> in the group. Prime graphs of solvable groups have been characterized in graph theoretical terms only, as have been the prime graphs of groups whose only nonsolvable composition factor is <span>(A_5)</span>. In this paper, we classify the prime graphs of all groups whose composition factors have arithmetically small orders, that is, have no more than three prime divisors in their orders. We find that all such graphs have 3-colorable complements, and we provide full characterizations of the prime graphs of such groups based on the exact type and multiplicity of the nonabelian composition factors of the group.\u0000</p>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain and its computation 给定接触角的曲线域平均曲率流的最小运动格式及其计算
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-11-18 DOI: 10.1007/s10231-023-01398-9
Tokuhiro Eto, Yoshikazu Giga
{"title":"On a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain and its computation","authors":"Tokuhiro Eto, Yoshikazu Giga","doi":"10.1007/s10231-023-01398-9","DOIUrl":"https://doi.org/10.1007/s10231-023-01398-9","url":null,"abstract":"<p>We introduce a capillary Chambolle-type scheme for mean curvature flow with prescribed contact angle. Our scheme includes a capillary functional instead of just the total variation. We show that the scheme is well-defined and has consistency with the energy minimizing scheme of Almgren–Taylor–Wang type. Moreover, for a planar motion in a strip, we give several examples of numerical computation of this scheme based on the split Bregman method instead of a duality method.</p>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Module braces: relations between the additive and the multiplicative groups 模括号：加法群和乘法群之间的关系
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-07-12 DOI: 10.1007/s10231-023-01349-4
Ilaria Del Corso
{"title":"Module braces: relations between the additive and the multiplicative groups","authors":"Ilaria Del Corso","doi":"10.1007/s10231-023-01349-4","DOIUrl":"10.1007/s10231-023-01349-4","url":null,"abstract":"<div><p>In this paper, we define a class of braces that we call module braces or <i>R</i>-braces, which are braces for which the additive group has also a module structure over a ring <i>R</i>, and for which the values of the gamma functions are automorphisms of <i>R</i>-modules. This class of braces has already been considered in the literature in the case where the ring <i>R</i> is a field; we generalise the definition to any ring <i>R</i>, reinterpreting it in terms of the so-called gamma function associated with the brace, and prove that this class of braces enjoys all the natural properties one can require. We exhibit explicit example of R-braces, and we study the splitting of a module braces in relation to the splitting of the ring <i>R</i>, generalising thereby Byott’s result on the splitting of a brace with nilpotent multiplicative group as a sum of its Sylow subgroups. The core of the paper is in the last two sections, in which, using methods from commutative algebra and number theory, we study the relations between the additive and the multiplicative groups of an <i>R</i>-brace showing that if a certain decomposition of the additive group is <i>small</i> (in some sense which depends on <i>R</i>), then the additive and the multiplicative groups have the same number of elements of each order. In some cases, this result considerably broadens the range of applications of the results already known on this issue.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01349-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50475105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interior dynamics of fatou sets fatou集的内部动力学
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-06-20 DOI: 10.1007/s10231-023-01344-9
Mi Hu
{"title":"Interior dynamics of fatou sets","authors":"Mi Hu","doi":"10.1007/s10231-023-01344-9","DOIUrl":"10.1007/s10231-023-01344-9","url":null,"abstract":"<div><p>In this paper, we investigate the precise behavior of orbits inside attracting basins. Let <i>f</i> be a holomorphic polynomial of degree <span>(mge 2)</span> in <span>(mathbb {C})</span>, <span>(mathcal {A}(p))</span> be the basin of attraction of an attracting fixed point <i>p</i> of <i>f</i>, and <span>(Omega _i (i=1, 2, cdots ))</span> be the connected components of <span>(mathcal {A}(p))</span>. Assume <span>(Omega _1)</span> contains <i>p</i> and <span>({f^{-1}(p)}cap Omega _1ne {p})</span>. Then there is a constant <i>C</i> so that for every point <span>(z_0)</span> inside any <span>(Omega _i)</span>, there exists a point <span>(qin cup _k f^{-k}(p))</span> inside <span>(Omega _i)</span> such that <span>(d_{Omega _i}(z_0, q)le C)</span>, where <span>(d_{Omega _i})</span> is the Kobayashi distance on <span>(Omega _i.)</span> In paper Hu (Dynamics inside parabolic basins, 2022), we proved that this result is not valid for parabolic basins.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01344-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50500124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Uniform convolution estimates for complex polynomial curves in ({mathbb {C}}^3) ｛mathbb｛C｝｝^3中复多项式曲线的一致卷积估计
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-06-16 DOI: 10.1007/s10231-023-01346-7
Conor Meade
{"title":"Uniform convolution estimates for complex polynomial curves in ({mathbb {C}}^3)","authors":"Conor Meade","doi":"10.1007/s10231-023-01346-7","DOIUrl":"10.1007/s10231-023-01346-7","url":null,"abstract":"<div><p>We establish optimal (<i>p</i>, <i>q</i>) ranges for the weighted convolution operator associated with a complex polynomial curve. Establishing this estimate comes down to establishing a lower bound for the Jacobian of a mapping associated with the complex curve in question.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01346-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50451167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classification of homogeneous hypersurfaces in some noncompact symmetric spaces of rank two 二阶非紧对称空间中齐次超曲面的分类
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-06-07 DOI: 10.1007/s10231-023-01345-8
Ivan Solonenko
{"title":"Classification of homogeneous hypersurfaces in some noncompact symmetric spaces of rank two","authors":"Ivan Solonenko","doi":"10.1007/s10231-023-01345-8","DOIUrl":"10.1007/s10231-023-01345-8","url":null,"abstract":"<div><p>We classify, up to isometric congruence, the homogeneous hypersurfaces in the Riemannian symmetric spaces <span>(textrm{SL}(3,mathbb {H})/textrm{Sp}(3), textrm{SO}(5,mathbb {C})/textrm{SO}(5),)</span> and <span>(textrm{Gr}^*(2,mathbb {C}^{n+4}) = textrm{SU}(n+2,2)/textrm{S}(textrm{U}(n+2)textrm{U}(2)), , n geqslant 1)</span>.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01345-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50459322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On maximal function of discrete rough truncated Hilbert transforms 关于离散粗糙截断Hilbert变换的极大函数
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-06-07 DOI: 10.1007/s10231-023-01340-z
Maciej Paluszyński, Jacek Zienkiewicz
{"title":"On maximal function of discrete rough truncated Hilbert transforms","authors":"Maciej Paluszyński,&nbsp;Jacek Zienkiewicz","doi":"10.1007/s10231-023-01340-z","DOIUrl":"10.1007/s10231-023-01340-z","url":null,"abstract":"<div><p>We prove the weak type (1,1) estimate for maximal function of the truncated rough Hilbert transform considered in Paluszy’nski (ASNSCS 910:679-704, 2019), Paluszy’nski (CM 164(2):305-325, 2021).</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01340-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50459321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New monotonicity formulas for the curve shortening flow in ({mathbb {R}}^3) 关于（｛mathbb｛R｝｝^3）中曲线缩短流的新单调性公式
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-06-02 DOI: 10.1007/s10231-023-01348-5
Hayk Mikayelyan
{"title":"New monotonicity formulas for the curve shortening flow in ({mathbb {R}}^3)","authors":"Hayk Mikayelyan","doi":"10.1007/s10231-023-01348-5","DOIUrl":"10.1007/s10231-023-01348-5","url":null,"abstract":"<div><p>For the curve shortening flow in <span>({mathbb {R}}^3)</span> several new monotonicity formulas are derived. All of them share one main feature: the dependence of the “energy” term on the angle between the position vector and the plane orthogonal to the tangent vector. The first formula deals with the projection of the curve on the unit sphere, and computes the derivative of its length. The second formula is the generalization of the classical formula of G. Huisken, while the third one is the generalization of the monotonicity formula with logarithmic terms previously derived by the author for planar curves.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01348-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50442315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reductions: precontact versus presymplectic 还原：预接触与预辛
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-06-02 DOI: 10.1007/s10231-023-01341-y
Katarzyna Grabowska, Janusz Grabowski
{"title":"Reductions: precontact versus presymplectic","authors":"Katarzyna Grabowska,&nbsp;Janusz Grabowski","doi":"10.1007/s10231-023-01341-y","DOIUrl":"10.1007/s10231-023-01341-y","url":null,"abstract":"<div><p>We show that contact reductions can be described in terms of symplectic reductions in the traditional Marsden–Weinstein–Meyer as well as the constant rank picture. The point is that we view contact structures as particular (homogeneous) symplectic structures. A group action by contactomorphisms is lifted to a Hamiltonian action on the corresponding symplectic manifold, called the symplectic cover of the contact manifold. In contrast to the majority of the literature in the subject, our approach includes general contact structures (not only co-oriented) and changes the traditional view point: contact Hamiltonians and contact moment maps for contactomorphism groups are no longer defined on the contact manifold itself, but on its symplectic cover. Actually, the developed framework for reductions is slightly more general than purely contact, and includes a precontact and presymplectic setting which is based on the observation that there is a one-to-one correspondence between isomorphism classes of precontact manifolds and certain homogeneous presymplectic manifolds.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01341-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50442316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
On the periodicity of an algorithm for p-adic continued fractions 关于p-adic连分式算法的周期性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-06-01 DOI: 10.1007/s10231-023-01347-6
Nadir Murru, Giuliano Romeo, Giordano Santilli
{"title":"On the periodicity of an algorithm for p-adic continued fractions","authors":"Nadir Murru,&nbsp;Giuliano Romeo,&nbsp;Giordano Santilli","doi":"10.1007/s10231-023-01347-6","DOIUrl":"10.1007/s10231-023-01347-6","url":null,"abstract":"<div><p>In this paper we study the properties of an algorithm, introduced in Browkin (Math Comput 70:1281–1292, 2000), for generating continued fractions in the field of <i>p</i>-adic numbers <span>(mathbb Q_p)</span>. First of all, we obtain an analogue of the Galois’ Theorem for classical continued fractions. Then, we investigate the length of the preperiod for periodic expansions of square roots. Finally, we prove that there exist infinitely many square roots of integers in <span>(mathbb Q_p)</span> that have a periodic expansion with period of length 4, solving an open problem left by Browkin in (Math Comput 70:1281–1292, 2000).\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01347-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50432805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
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