On characters and fixed points of coprime operator groups

DOI10.1016/0021-8693(90)90179-RzbMath0703.20023MaRDI QIDQ915857

I. M. Isaacs, Brian Hartley

Publication date: 1990

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

zbMATH Keywords

Fitting heightscharactersrepresentationsfinite soluble groupsirreducible characterslocally finite groupsmultiplicitiesirreducible componentschains of subgroupstensor products of modulesfactorization theoremslengthsfixed points of automorphismsdirect products of extraspecial groupsfinite groups of operators

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Periodic groups; locally finite groups (20F50) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Automorphisms of abstract finite groups (20D45)

Related Items (13)

Finite groups with an automorphism of prime order whose centralizer has small rank. ⋮ Unnamed Item ⋮ Coprime automorphisms of finite groups ⋮ On the rank of a finite group of odd order with an involutory automorphism ⋮ Good action on a finite group ⋮ Finite groups with a soluble group of coprime automorphisms whose fixed points have bounded Engel sinks ⋮ Finite groups admitting a coprime automorphism satisfying an additional polynomial identity ⋮ Finite groups and Lie rings with a metacyclic Frobenius group of automorphisms. ⋮ Finite Groups and Lie Rings with an Automorphism of Order 2ⁿ ⋮ On finite soluble groups with almost fixed-point-free automorphisms of noncoprime order. ⋮ Frobenius groups of automorphisms with almost fixed point free kernel ⋮ Almost regular automorphisms ⋮ Rank and order of a finite group admitting a Frobenius-like group of automorphisms.

Cites Work

• Unnamed Item
• Unnamed Item
• Fitting height of groups and of fixed points
• Generic fixed point free action of arbitrary finite groups
• Carter subgroups and Fitting heights of finite solvable groups
• A NOTE ON FIXED-POINT-FREE ACTIONS OF FINITE GROUPS
• Fixed point free action with regular orbits.
• Finite soluble groups admitting an automorphism of prime power order with few fixed points
• Characters of Solvable and Symplectic Groups
• Endliche Gruppen I
• Tensor Products of Representations of Finite Groups

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