Indices of elements and normal structure of finite groups.

DOI10.1016/j.jalgebra.2004.10.003zbMath1112.20021OpenAlexW2080567278MaRDI QIDQ1763739

Lev S. Kazarin, Yakov G. Berkovich

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.10.003

zbMATH Keywords

conjugacy classesfinite groupscharactersSylow subgroupsnilpotencyelements of prime power orderconjugacy class sizes

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Ordinary representations and characters (20C15) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60)

Related Items (26)

THE INFLUENCE OF CONJUGACY CLASS SIZES ON THE STRUCTURE OF FINITE GROUPS: A SURVEY ⋮ Finite groups with given systems of weakly \(S\)-propermutable subgroups ⋮ Unnamed Item ⋮ On the conjugacy class lengths of finite groups. ⋮ On an extension of a theorem on conjugacy class sizes. ⋮ Squares of real conjugacy classes in finite groups ⋮ On groups whose small-order elements generate a small subgroup. ⋮ On the normal subgroup with coprime \(G\)-conjugacy class sizes ⋮ Remarks on the supersolvability of a group with prime indices of some subgroups ⋮ Unnamed Item ⋮ Prime power indices in factorised groups ⋮ On zeros of irreducible characters lying in a normal subgroup ⋮ \(\mathfrak{F}_{\tau}\)-embedded and \(\mathfrak{F}_{\tau\phi}\)-embedded subgroups of finite groups ⋮ Onm-S-supplemented subgroups of finite groups ⋮ On the normal subgroup with minimal \(G\)-conjugacy class sizes ⋮ A note on conjugacy class sizes of finite groups. ⋮ Finite groups with three conjugacy class sizes of some elements. ⋮ Some problems about products of conjugacy classes in finite groups ⋮ On the centralizers of the \(p\)-regular elements in a finite group ⋮ Products of groups and class sizes of \(\pi \)-elements ⋮ On coprime \(G\)-conjugacy class sizes in a normal subgroup. ⋮ On Conjugacy Class Sizes of the p′-Elements with Prime Power Order ⋮ Groups whose vanishing class sizes are prime powers ⋮ Factorizations of groups and related topics. ⋮ Finite groups with generalized Ore supplement conditions for primary subgroups. ⋮ Some Conditions Under which a Finite Group Belongs to a Baer-Local Formation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the length of the conjugacy classes of finite groups
• Groups of prime power order. Vol. 1.
• On character degrees quotients
• Number of Sylow subgroups and \(p\)-nilpotence of finite groups
• Burnside's \(p^ \alpha\)-lemma
• Solvability of groups of odd order
• Equally partitioned groups
• Über den Frobenius'schen Klassenbegriff in nilpotenten Gruppen
• On the p -Length of p -Soluble Groups and Reduction Theorems for Burnside's Problem
• Implications of conjugacy class size
• Some corollaries of Frobenius’ normal 𝑝-complement theorem
• Group Elements of Prime Power Index
• On Finite Groups with Given Conjugate Types I

This page was built for publication: Indices of elements and normal structure of finite groups.