Journal of Group Theory最新文献

{"title":"Automorphic word maps and the Amit–Ashurst conjecture","authors":"Harish Kishnani, Amit Kulshrestha","doi":"10.1515/jgth-2023-0151","DOIUrl":"https://doi.org/10.1515/jgth-2023-0151","url":null,"abstract":"In this article, we address the Amit–Ashurst conjecture on lower bounds of a probability distribution associated to a word on a finite nilpotent group. We obtain an extension of a result of [R. D. Camina, A. Iñiguez and A. Thillaisundaram, Word problems for finite nilpotent groups, <jats:italic>Arch. Math. (Basel)</jats:italic> 115 (2020), 6, 599–609] by providing improved bounds for the case of finite nilpotent groups of class 2 for words in an arbitrary number of variables, and also settle the conjecture in some cases. We achieve this by obtaining words that are identically distributed on a group to a given word. In doing so, we also obtain an improvement of a result of [A. Iñiguez and J. Sangroniz, Words and characters in finite 𝑝-groups, <jats:italic>J. Algebra</jats:italic> 485 (2017), 230–246] using elementary techniques.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757141","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":"The relational complexity of linear groups acting on subspaces","authors":"Saul D. Freedman, Veronica Kelsey, Colva M. Roney-Dougal","doi":"10.1515/jgth-2023-0262","DOIUrl":"https://doi.org/10.1515/jgth-2023-0262","url":null,"abstract":"The relational complexity of a subgroup 𝐺 of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>Sym</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi mathvariant=\"normal\">Ω</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0262_ineq_0001.png\" /> <jats:tex-math>mathrm{Sym}({Omega})</jats:tex-math> </jats:alternatives> </jats:inline-formula> is a measure of the way in which the orbits of 𝐺 on <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi mathvariant=\"normal\">Ω</m:mi> <m:mi>k</m:mi> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0262_ineq_0002.png\" /> <jats:tex-math>Omega^{k}</jats:tex-math> </jats:alternatives> </jats:inline-formula> for various 𝑘 determine the original action of 𝐺. Very few precise values of relational complexity are known. This paper determines the exact relational complexity of all groups lying between <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mi>PSL</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi mathvariant=\"double-struck\">F</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0262_ineq_0003.png\" /> <jats:tex-math>mathrm{PSL}_{n}(mathbb{F})</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mi>PGL</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi mathvariant=\"double-struck\">F</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0262_ineq_0004.png\" /> <jats:tex-math>mathrm{PGL}_{n}(mathbb{F})</jats:tex-math> </jats:alternatives> </jats:inline-formula>, for an arbitrary field 𝔽, acting on the set of 1-dimensional subspaces of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi mathvariant=\"double-struck\">F</m:mi> <m:mi>n</m:mi> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0262_ineq_0005.png\" /> <jats:tex-math>mathbb{F}^{n}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. We also bound the relational complexity of all groups lying between <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mi>PSL</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>q<","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757226","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":"The central tree property and algorithmic problems on subgroups of free groups","authors":"Mallika Roy, Enric Ventura, Pascal Weil","doi":"10.1515/jgth-2023-0050","DOIUrl":"https://doi.org/10.1515/jgth-2023-0050","url":null,"abstract":"We study the average case complexity of the Uniform Membership Problem for subgroups of free groups, and we show that it is orders of magnitude smaller than the worst case complexity of the best known algorithms. This applies to subgroups given by a fixed number of generators as well as to subgroups given by an exponential number of generators. The main idea behind this result is to exploit a generic property of tuples of words, called the central tree property. An application is given to the average case complexity of the Relative Primitivity Problem, using Shpilrain’s recent algorithm to decide primitivity, whose average case complexity is a constant depending only on the rank of the ambient free group.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757282","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":"Finite normal subgroups of strongly verbally closed groups","authors":"Filipp D. Denissov","doi":"10.1515/jgth-2023-0015","DOIUrl":"https://doi.org/10.1515/jgth-2023-0015","url":null,"abstract":"In a recent paper by A. A. Klyachko, V. Y. Miroshnichenko, and A. Y. Olshanskii, it is proven that the center of any finite strongly verbally closed group is a direct factor. In this paper, we extend this result to the case of finite normal subgroups of any strongly verbally closed group. It follows that finitely generated nilpotent groups with nonabelian torsion subgroups are not strongly verbally closed.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757140","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":"Groups with subnormal or modular Schmidt 𝑝𝑑-subgroups","authors":"Victor S. Monakhov, Irina L. Sokhor","doi":"10.1515/jgth-2023-0096","DOIUrl":"https://doi.org/10.1515/jgth-2023-0096","url":null,"abstract":"A Schmidt group is a finite non-nilpotent group such that every proper subgroup is nilpotent. In this paper, we prove that if every Schmidt subgroup of a finite group 𝐺 is subnormal or modular, then <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>G</m:mi> <m:mo>/</m:mo> <m:mi>F</m:mi> </m:mrow> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>G</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0096_ineq_0001.png\" /> <jats:tex-math>G/F(G)</jats:tex-math> </jats:alternatives> </jats:inline-formula> is cyclic. Moreover, for a given prime 𝑝, we describe the structure of finite groups with subnormal or modular Schmidt subgroups of order divisible by 𝑝.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757568","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":"Realizing finite groups as automizers","authors":"Sylvia Bayard, Justin Lynd","doi":"10.1515/jgth-2022-0145","DOIUrl":"https://doi.org/10.1515/jgth-2022-0145","url":null,"abstract":"It is shown that any finite group 𝐴 is realizable as the automizer in a finite perfect group 𝐺 of an abelian subgroup whose conjugates generate 𝐺. The construction uses techniques from fusion systems on arbitrary finite groups, most notably certain realization results for fusion systems of the type studied originally by Park.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757138","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":"The algebraic entropy of one-dimensional finitary linear cellular automata","authors":"Hasan Akın, Dikran Dikranjan, Anna Giordano Bruno, Daniele Toller","doi":"10.1515/jgth-2023-0092","DOIUrl":"https://doi.org/10.1515/jgth-2023-0092","url":null,"abstract":"The aim of this paper is to present one-dimensional finitary linear cellular automata 𝑆 on <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi mathvariant=\"double-struck\">Z</m:mi> <m:mi>m</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0092_ineq_0001.png\" /> <jats:tex-math>mathbb{Z}_{m}</jats:tex-math> </jats:alternatives> </jats:inline-formula> from an algebraic point of view. Among various other results, we (i) show that the Pontryagin dual <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mover accent=\"true\"> <m:mi>S</m:mi> <m:mo>̂</m:mo> </m:mover> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0092_ineq_0002.png\" /> <jats:tex-math>hat{S}</jats:tex-math> </jats:alternatives> </jats:inline-formula> of 𝑆 is a classical one-dimensional linear cellular automaton 𝑇 on <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi mathvariant=\"double-struck\">Z</m:mi> <m:mi>m</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0092_ineq_0001.png\" /> <jats:tex-math>mathbb{Z}_{m}</jats:tex-math> </jats:alternatives> </jats:inline-formula>; (ii) give several equivalent conditions for 𝑆 to be invertible with inverse a finitary linear cellular automaton; (iii) compute the algebraic entropy of 𝑆, which coincides with the topological entropy of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>T</m:mi> <m:mo>=</m:mo> <m:mover accent=\"true\"> <m:mi>S</m:mi> <m:mo>̂</m:mo> </m:mover> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0092_ineq_0004.png\" /> <jats:tex-math>T=hat{S}</jats:tex-math> </jats:alternatives> </jats:inline-formula> by the so-called Bridge Theorem. In order to better understand and describe entropy, we introduce the degree <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>deg</m:mi> <m:mo>⁡</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>S</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0092_ineq_0005.png\" /> <jats:tex-math>deg(S)</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>deg</m:mi> <m:mo>⁡</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>T</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0092_ineq_0006.png\" /> <jats:tex-mat","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139647210","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":"Units, zero-divisors and idempotents in rings graded by torsion-free groups","authors":"Johan Öinert","doi":"10.1515/jgth-2023-0110","DOIUrl":"https://doi.org/10.1515/jgth-2023-0110","url":null,"abstract":"The three famous problems concerning units, zero-divisors and idempotents in group rings of torsion-free groups, commonly attributed to Kaplansky, have been around for more than 60 years and still remain open in characteristic zero. In this article, we introduce the corresponding problems in the considerably more general context of arbitrary rings graded by torsion-free groups. For natural reasons, we will restrict our attention to rings without non-trivial homogeneous zero-divisors with respect to the given grading. We provide a partial solution to the extended problems by solving them for rings graded by unique product groups. We also show that the extended problems exhibit the same (potential) hierarchy as the classical problems for group rings. Furthermore, a ring which is graded by an arbitrary torsion-free group is shown to be indecomposable, and to have no non-trivial central zero-divisor and no non-homogeneous central unit. We also present generalizations of the classical group ring conjectures.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139554853","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":"Multiple transitivity except for a system of imprimitivity","authors":"Colin D. Reid","doi":"10.1515/jgth-2023-0062","DOIUrl":"https://doi.org/10.1515/jgth-2023-0062","url":null,"abstract":"Let Ω be a set equipped with an equivalence relation <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mo>∼</m:mo> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0062_ineq_0001.png\" /> <jats:tex-math>sim</jats:tex-math> </jats:alternatives> </jats:inline-formula>; we refer to the equivalence classes as blocks of Ω. A permutation group <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>G</m:mi> <m:mo>≤</m:mo> <m:mrow> <m:mi>Sym</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi mathvariant=\"normal\">Ω</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0062_ineq_0002.png\" /> <jats:tex-math>Gleqmathrm{Sym}(Omega)</jats:tex-math> </jats:alternatives> </jats:inline-formula> is <jats:italic>𝑘-by-block-transitive</jats:italic> if <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mo>∼</m:mo> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0062_ineq_0001.png\" /> <jats:tex-math>sim</jats:tex-math> </jats:alternatives> </jats:inline-formula> is 𝐺-invariant, with at least 𝑘 blocks, and 𝐺 is transitive on the set of 𝑘-tuples of points such that no two entries lie in the same block. The action is <jats:italic>block-faithful</jats:italic> if the action on the set of blocks is faithful. In this article, we classify the finite block-faithful 2-by-block-transitive actions. We also show that, for <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>k</m:mi> <m:mo>≥</m:mo> <m:mn>3</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0062_ineq_0004.png\" /> <jats:tex-math>kgeq 3</jats:tex-math> </jats:alternatives> </jats:inline-formula>, there are no finite block-faithful 𝑘-by-block-transitive actions with nontrivial blocks.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139496858","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":"Action of automorphisms on irreducible characters of finite reductive groups of type 𝖠","authors":"Farrokh Shirjian, Ali Iranmanesh, Farideh Shafiei","doi":"10.1515/jgth-2022-0034","DOIUrl":"https://doi.org/10.1515/jgth-2022-0034","url":null,"abstract":"Let 𝐺 be a finite reductive group such that the derived subgroup of the underlying algebraic group is a product of quasi-simple groups of type 𝖠. In this paper, we give an explicit description of the action of automorphisms of 𝐺 on the set of its irreducible complex characters. This generalizes a recent result of M. Cabanes and B. Späth [Equivariant character correspondences and inductive McKay condition for type 𝖠, <jats:italic>J. Reine Angew. Math.</jats:italic> 728 (2017), 153–194] and provides a useful tool for investigating the local sides of the local-global conjectures as one usually needs to deal with Levi subgroups. As an application we obtain a generalization of the stabilizer condition in the so-called inductive McKay condition [B. Späth, Inductive McKay condition in defining characteristic, <jats:italic>Bull. Lond. Math. Soc.</jats:italic> 44 (2012), 3, 426–438; Theorem 2.12] for irreducible characters of 𝐺. Moreover, a criterion is given to explicitly determine whether an irreducible character is a constituent of a given generalized Gelfand–Graev character of 𝐺.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139476967","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}