On the probability that a group element is \(p\)-singular

DOI10.1006/jabr.1995.1238zbMath0835.20006OpenAlexW2128861872MaRDI QIDQ1899090

I. M. Isaacs, Nicolas Spaltenstein, William M. Kantor

Publication date: 10 April 1996

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

Full work available at URL: https://doi.org/10.1006/jabr.1995.1238

zbMATH Keywords

sporadic groupsprobabilitypermutation groupsgroups of Lie typesimple groupsalmost simple groupsprimitive groups\(p\)-singular elementssharply 2-transitive groups

Mathematics Subject Classification ID

Finite simple groups and their classification (20D05) Subgroups of symmetric groups (20B35) Probabilistic methods in group theory (20P05)

Related Items (16)

Finding involutions in finite Lie type groups of odd characteristic. ⋮ Variations of Landau's theorem for \(p\)-regular and \(p\)-singular conjugacy classes. ⋮ Proportions of elements with given 2-part order in finite classical groups of odd characteristic. ⋮ ALGORITHMS TO IDENTIFY ABUNDANTp-SINGULAR ELEMENTS IN FINITE CLASSICAL GROUPS ⋮ Adjoint representations of black box groups \(\operatorname{PSL}_2(\mathbb{F}_q)\) ⋮ Symmetric functions, generalized blocks, and permutations with restricted cycle structure ⋮ Abundant \(p\)-singular elements in finite classical groups. ⋮ Black box exceptional groups of Lie type. II. ⋮ Constructive membership in black-box groups ⋮ Random matrix theory over finite fields ⋮ Estimating proportions of elements in finite groups of Lie type. ⋮ Random generation of finite simple groups by \(p\)-regular or \(p\)-singular elements ⋮ Permutations with orders coprime to a given integer ⋮ CONSTRUCTIVE RECOGNITION OF NORMALIZERS OF SMALL EXTRA-SPECIAL MATRIX GROUPS ⋮ On the Number ofp-Regular Elements in Finite Simple Groups ⋮ Finite affine groups: cycle indices, Hall-Littlewood polynomials, and probabilistic algorithms

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