A theorem on random matrices and some applications

DOI10.1006/jabr.1997.7167zbMath0910.20031OpenAlexW2082580451MaRDI QIDQ1379068

Aner Shalev

Publication date: 20 April 1999

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1997.7167

zbMATH Keywords

general linear groupsmaximal subgroupsrandom matricesclassical groupsspecial linear groupsirreducible subgroupsgenerating pairs

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Asymptotic results on counting functions for algebraic and topological structures (11N45) Random matrices (algebraic aspects) (15B52) Probabilistic methods in group theory (20P05)

Related Items (14)

Invariable generation of prosoluble groups. ⋮ Products of derangements in simple permutation groups ⋮ Generating sets of finite groups ⋮ Derangements in subspace actions of finite classical groups ⋮ Covering and growth for group subsets and representations ⋮ Invariable generation and the Chebotarev invariant of a finite group. ⋮ On the probability of generating invariably a finite simple group ⋮ Cycle indices for finite orthogonal groups of even characteristic ⋮ Derangements in finite classical groups for actions related to extension field and imprimitive subgroups and the solution of the Boston–Shalev conjecture ⋮ Random matrix theory over finite fields ⋮ On fixed points of permutations. ⋮ Minimal invariable generating sets ⋮ The place of exceptional covers among all diophantine relations ⋮ Coprime invariable generation and minimal-exponent groups.

Cites Work

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• On the Orders of Maximal Subgroups of the Finite Classical Groups
• A Recognition Algorithm for Special Linear Groups
• The probability of generating a classical group
• Random Permutations: Some Group-Theoretic Aspects
• On Random Generation of the Symmetric Group
• Random Generation of Simple Groups by Two Conjugate Elements
• On the conjugacy classes in the unitary, symplectic and orthogonal groups

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