Representation growth in positive characteristic and conjugacy classes of maximal subgroups.

DOI10.1215/00127094-1507300zbMath1244.20007arXiv1009.2437OpenAlexW2126966591MaRDI QIDQ662419

Robert M. Guralnick, Michael J. Larsen, Pham Hũ'u Tiêp

Publication date: 22 February 2012

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.2437

zbMATH Keywords

conjugacy classesmaximal subgroupssimple algebraic groupsfinite almost simple groupsnumbers of irreducible representationsrepresentation growth

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Linear algebraic groups over arbitrary fields (20G15) Representations of finite symmetric groups (20C30) Maximal subgroups (20E28) Representation theory for linear algebraic groups (20G05) Modular representations and characters (20C20) Simple groups: alternating groups and groups of Lie type (20D06) Representations of finite groups of Lie type (20C33)

Related Items

THE -INVARIANT AND THOMPSON’S CONJECTURE, Surjective word maps and Burnside's \(p^aq^b\) theorem, Irreducible restrictions of representations of symmetric and alternating groups in small characteristics, Growth of cross-characteristic representations of finite quasisimple groups of Lie type., Invariable generation and the Chebotarev invariant of a finite group., On the probability of generating invariably a finite simple group, Low degree representations of simple Lie groups, Representation of finite groups: conjectures, reductions, and applications., Probabilistic Waring problems for finite simple groups, Lower bounds for dimensions of irreducible representations of symmetric groups, Probabilistic and Asymptotic Aspects of Finite Simple Groups

Cites Work

• Unnamed Item
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• On the maximal subgroups of the finite classical groups
• Solvable generation of groups and Sylow subgroups of the lower central series
• Irreducible modules and parabolic subgroups
• On the minimal degrees of projective representations of the finite Chevalley groups
• A proof of the Mullineux conjecture
• On residue symbols and the Mullineux conjecture
• On the minimal degrees of projective representations of the finite Chevalley groups. II
• On conjugacy classes of maximal subgroups of finite simple groups, and a related zeta function.
• Representation growth of linear groups
• On a conjecture of G. E. Wall.
• SMALLEST DEGREES OF REPRESENTATIONS OF EXCEPTIONAL GROUPS OF LIE TYPE
• Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements
• On the minimal dimensions of irreducible representations of symmetric groups
• WEIGHTS OF INFINITESIMALLY IRREDUCIBLE REPRESENTATIONS OF CHEVALLEY GROUPS OVER A FIELD OF PRIME CHARACTERISTIC
• Bijections of p -Regular Partitions and p -Modular Irreducibles of the Symmetric Groups
• The probability of generating a classical group
• Branching rules for modular representations of symmetric groups, II.
• On restrictions of modular spin representations of symmetric and alternating groups
• Character degrees and random walks in finite groups of Lie type
• Low degree representations of simple Lie groups
• Introduction to Lie Algebras and Representation Theory