On the number of conjugacy classes of a finite group

DOI10.1006/jabr.1993.1196zbMath0830.20048OpenAlexW2012818805MaRDI QIDQ1320136

L. G. Kovács, Geoffrey R. Robinson

Publication date: 7 June 1994

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

Full work available at URL: https://doi.org/10.1006/jabr.1993.1196

zbMATH Keywords

defect groupsprimitive permutation groups\(p\)-blockssolvable subgroupsalmost simple groupsclassification of finite simple groupssubgroups of symmetric groupsnumber of irreducible ordinary characters\(kGV\)-problemfinite subgroups of \(\text{GL}(r,\mathbb{C})\)number of characters in \(p\)-blocksnumber of conjugacy classes of finite groups

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Modular representations and characters (20C20) Subgroups of symmetric groups (20B35)

Related Items (24)

On the number of conjugacy classes of a primitive permutation group ⋮ Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements ⋮ The solution of the \(k(GV)\)-problem. ⋮ THE INFLUENCE OF CONJUGACY CLASS SIZES ON THE STRUCTURE OF FINITE GROUPS: A SURVEY ⋮ Nilpotent injectors and conjugacy classes in solvable groups ⋮ Fixed conjugacy classes of normal subgroups and the \(k(GV)\)-problem. ⋮ Upper bounds for the number of conjugacy classes of a finite group ⋮ Enumerating finite racks, quandles and kei ⋮ On the orders of composition factors in completely reducible groups ⋮ Real vectors for linear groups and the \(k(GV)\)-problem ⋮ On the non-coprime \(k(GV)\)-problem. ⋮ THE CONTRIBUTION OF L. G. KOVÁCS TO THE THEORY OF PERMUTATION GROUPS ⋮ THE WORK OF L. G. KOVÁCS ON REPRESENTATION THEORY ⋮ THE GRADED CENTER OF A TRIANGULATED CATEGORY ⋮ Bounds on the largest Kronecker and induced multiplicities of finite groups ⋮ Signed permutation modules, Singer cycles and class numbers ⋮ Permutation groups, minimal degrees and quantum computing. ⋮ On Brauer's \(k(B)\)-problem for blocks of \(p\)-solvable groups with non-Abelian defect groups. ⋮ On the commuting probability in finite groups. ⋮ A generalization of the diameter bound of Liebeck and Shalev for finite simple groups ⋮ On finite simply reducible groups ⋮ Conjugacy class numbers and \(\pi \)-subgroups ⋮ The non-coprime \(k(GV)\) problem. ⋮ On the number of conjugacy classes of a permutation group.

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