Bulletin of the London Mathematical Society最新文献

{"title":"On the length of nonsolutions to equations with constants in some linear groups","authors":"Henry Bradford, Jakob Schneider, Andreas Thom","doi":"10.1112/blms.13058","DOIUrl":"https://doi.org/10.1112/blms.13058","url":null,"abstract":"<p>We show that for any finite-rank–free group <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math>, any word-equation in one variable of length <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> with constants in <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math> fails to be satisfied by some element of <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math> of word-length <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>O</mi>\u0000 <mo>(</mo>\u0000 <mi>log</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$O(log (n))$</annotation>\u0000 </semantics></math>. By a result of the first author, this logarithmic bound cannot be improved upon for any finitely generated group <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math>. Beyond free groups, our method (and the logarithmic bound) applies to a class of groups including <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>PSL</mo>\u0000 <mi>d</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$operatorname{PSL}_d(mathbb {Z})$</annotation>\u0000 </semantics></math> for all <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$d geqslant 2$</annotation>\u0000 </semantics></math>, and the fundamental groups of all closed hyperbolic surfaces and 3-manifolds. Finally, using a construction of Nekrashevych, we exhibit a finitely generated group <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math> and a sequence of word-equations  with constants in <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math> for which every nonsolution in <span></span><math>\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 7","pages":"2338-2349"},"PeriodicalIF":0.8,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13058","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141556540","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}

{"title":"Sobolev inequality on manifolds with asymptotically nonnegative Bakry–Émery Ricci curvature","authors":"Yuxin Dong,&nbsp;Hezi Lin,&nbsp;Lingen Lu","doi":"10.1112/blms.13061","DOIUrl":"https://doi.org/10.1112/blms.13061","url":null,"abstract":"<p>In this paper, inspired by Brendle (Comm. Pure Appl. Math. <b>76</b> (2023), 2192) and Johne (arXiv:2103.08496, 2021), we prove a Sobolev inequality on manifolds with density and asymptotically nonnegative Bakry–Émery Ricci curvature.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 7","pages":"2395-2407"},"PeriodicalIF":0.8,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141556539","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}

{"title":"Broué's abelian defect group conjecture for blocks with cyclic hyperfocal subgroups","authors":"Xueqin Hu,&nbsp;Kun Zhang,&nbsp;Yuanyang Zhou","doi":"10.1112/blms.13051","DOIUrl":"10.1112/blms.13051","url":null,"abstract":"<p>In this paper, we prove that the hyperfocal subalgebra of a block with an abelian defect group and a cyclic hyperfocal subgroup is Rickard equivalent to the group algebra of the semidirect of the hyperfocal subgroup by the inertial quotient of the block. In particular, the hyperfocal subalgebra is a Brauer tree algebra, which is analogous to the structure of blocks with cyclic defect groups. As a consequence, we show that Broué's abelian defect group conjecture holds for blocks with cyclic hyperfocal subgroups.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 6","pages":"2188-2211"},"PeriodicalIF":0.9,"publicationDate":"2024-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141012983","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}

{"title":"On the trace fields of hyperbolic Dehn fillings","authors":"Stavros Garoufalidis,&nbsp;BoGwang Jeon","doi":"10.1112/blms.13059","DOIUrl":"https://doi.org/10.1112/blms.13059","url":null,"abstract":"<p>Assuming Lehmer's conjecture, we estimate the degree of the trace field <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>/</mo>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$K(M_{p/q})$</annotation>\u0000 </semantics></math> of a hyperbolic Dehn filling <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>/</mo>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$M_{p/q}$</annotation>\u0000 </semantics></math> of a 1-cusped hyperbolic 3-manifold <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> by\u0000\u0000 </p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 7","pages":"2350-2373"},"PeriodicalIF":0.8,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13059","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141556541","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}

{"title":"On a multiplier operator induced by the Schwarzian derivative of univalent functions","authors":"Jianjun Jin","doi":"10.1112/blms.13056","DOIUrl":"https://doi.org/10.1112/blms.13056","url":null,"abstract":"<p>In this paper, we study a multiplier operator which is induced by the Schwarzian derivative of univalent functions with a quasiconformal extension to the extended complex plane. As applications, we show that the Brennan conjecture is satisfied for a large class of quasidisks. We also establish a new characterization of asymptotically conformal curves and of the Weil–Petersson curves in terms of the multiplier operator.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 7","pages":"2296-2314"},"PeriodicalIF":0.8,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141556735","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}

{"title":"Bounding toric singularities with normalized volume","authors":"Joaquín Moraga,&nbsp;Hendrik Süß","doi":"10.1112/blms.13052","DOIUrl":"https://doi.org/10.1112/blms.13052","url":null,"abstract":"<p>We study the normalized volume of toric singularities. As it turns out, there is a close relation to the notion of (nonsymmetric) Mahler volume from convex geometry. This observation allows us to use standard tools from convex geometry, such as the Blaschke–Santaló inequality and Radon's theorem to prove nontrivial facts about the normalized volume in the toric setting. For example, we prove that for every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ε</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$epsilon &amp;gt; 0$</annotation>\u0000 </semantics></math> there are only finitely many <span></span><math>\u0000 <semantics>\u0000 <mi>Q</mi>\u0000 <annotation>$mathbb {Q}$</annotation>\u0000 </semantics></math>-Gorenstein toric singularities with normalized volume at least <span></span><math>\u0000 <semantics>\u0000 <mi>ε</mi>\u0000 <annotation>$epsilon$</annotation>\u0000 </semantics></math>. From this result it directly follows that there are also only finitely many toric Sasaki–Einstein manifolds of volume at least <span></span><math>\u0000 <semantics>\u0000 <mi>ε</mi>\u0000 <annotation>$epsilon$</annotation>\u0000 </semantics></math> in each dimension. Additionally, we show that the normalized volume of every toric singularity is bounded from above by that of the rational double point of the same dimension. Finally, we discuss certain bounds of the normalized volume in terms of topological invariants of resolutions of the singularity. We establish two upper bounds in terms of the Euler characteristic and of the first Chern class, respectively. We show that a lower bound, which was conjectured earlier by He, Seong, and Yau, is closely related to the nonsymmetric Mahler conjecture in convex geometry.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 6","pages":"2212-2229"},"PeriodicalIF":0.9,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13052","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141251263","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}

{"title":"On noncommutative distributional Khintchine type inequalities","authors":"Yong Jiao,&nbsp;Xingyan Quan,&nbsp;Fedor Sukochev,&nbsp;Dmitriy Zanin","doi":"10.1112/blms.13055","DOIUrl":"https://doi.org/10.1112/blms.13055","url":null,"abstract":"&lt;p&gt;The purpose of this paper is to provide distributional estimates for the series of the form &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mo&gt;∑&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;⊗&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$sum _{k=1}^infty x_kotimes r_k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$lbrace x_krbrace _{kgeqslant 1}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; being elements from noncommutative Lorentz spaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;log&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Lambda _{log ^{1/2}}(mathcal {M})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$lbrace r_krbrace _{kgeqslant 1}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; bein","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 7","pages":"2278-2295"},"PeriodicalIF":0.8,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13055","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141556696","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}

{"title":"Stability estimates for the Vlasov–Poisson system in \u0000 \u0000 p\u0000 $p$\u0000 -kinetic Wasserstein distances","authors":"Mikaela Iacobelli,&nbsp;Jonathan Junné","doi":"10.1112/blms.13053","DOIUrl":"https://doi.org/10.1112/blms.13053","url":null,"abstract":"<p>We extend Loeper's <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math>-estimate (Theorem 2.9 in <i>J. Math. Pures Appl</i>. (9) <b>86</b> (2006), no. 1, 68–79) relating the force fields to the densities for the Vlasov–Poisson system to <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$L^p$</annotation>\u0000 </semantics></math>, with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>p</mi>\u0000 <mo>&lt;</mo>\u0000 <mo>+</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$1 &amp;lt; p &amp;lt;+infty$</annotation>\u0000 </semantics></math>, based on the Helmholtz–Weyl decomposition. This allows us to generalize both the classical Loeper's 2-Wasserstein stability estimate (Theorem 1.2 in <i>J. Math. Pures Appl</i>. (9) <b>86</b> (2006), no. 1, 68–79) and the recent stability estimate by the first author relying on the newly introduced kinetic Wasserstein distance (Theorem 3.1 in <i>Arch Rational Mech. Anal</i>. <b>244</b> (2022), no. 1, 27–50) to kinetic Wasserstein distances of order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>p</mi>\u0000 <mo>&lt;</mo>\u0000 <mo>+</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$1 &amp;lt;p&amp;lt;+infty$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 7","pages":"2250-2267"},"PeriodicalIF":0.8,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13053","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141556697","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}

{"title":"A note on \u0000 \u0000 r\u0000 $r$\u0000 -gaps between zeros of the Riemann zeta-function","authors":"Shōta Inoue","doi":"10.1112/blms.13054","DOIUrl":"https://doi.org/10.1112/blms.13054","url":null,"abstract":"<p>In this paper, we prove Selberg's announced result on <span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-gaps between zeros of the Riemann zeta-function <span></span><math>\u0000 <semantics>\u0000 <mi>ζ</mi>\u0000 <annotation>$zeta$</annotation>\u0000 </semantics></math>. Our proof uses a result on variations of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>arg</mo>\u0000 <mi>ζ</mi>\u0000 </mrow>\u0000 <annotation>$arg zeta$</annotation>\u0000 </semantics></math> by Tsang based on Selberg's method. The same result with explicit constants under the Riemann Hypothesis has been obtained by Conrey and Turnage-Butterbaugh using a different method. We explain how to obtain explicit constants under the Riemann Hypothesis using our approach which is based on Selberg's and Tsang's arguments.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 7","pages":"2268-2277"},"PeriodicalIF":0.8,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141556736","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}

{"title":"A class of rearrangement groups that are not invariably generated","authors":"Davide Perego,&nbsp;Matteo Tarocchi","doi":"10.1112/blms.13046","DOIUrl":"https://doi.org/10.1112/blms.13046","url":null,"abstract":"<p>A group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is invariably generated if there exists a subset <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mo>⊆</mo>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation>$S subseteq G$</annotation>\u0000 </semantics></math> such that, for every choice <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>g</mi>\u0000 <mi>s</mi>\u0000 </msub>\u0000 <mo>∈</mo>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation>$g_s in G$</annotation>\u0000 </semantics></math> for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 <mo>∈</mo>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation>$s in S$</annotation>\u0000 </semantics></math>, the group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is generated by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <msup>\u0000 <mi>s</mi>\u0000 <msub>\u0000 <mi>g</mi>\u0000 <mi>s</mi>\u0000 </msub>\u0000 </msup>\u0000 <mo>∣</mo>\u0000 <mi>s</mi>\u0000 <mo>∈</mo>\u0000 <mi>S</mi>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$lbrace s^{g_s} mid s in S rbrace$</annotation>\u0000 </semantics></math>. Gelander, Golan, and Juschenko (<i>J. Algebra</i> <b>478</b> (2016), 261–270) showed that Thompson groups <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mi>V</mi>\u0000 <annotation>$V$</annotation>\u0000 </semantics></math> are not invariably generated. Here, we generalize this result to the larger setting of rearrangement groups, proving that any subgroup of a rearrangement group that has a certain transitive property is not invariably generated.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 6","pages":"2115-2131"},"PeriodicalIF":0.9,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141251513","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}