c p -normality and coprime action in finite groups
Abstract
Let G and A be finite groups of coprime orders, with A acting on G via automorphisms. In this context of coprime action, an A-invariant subgroup H of G is called ACp-normal in G if there exists an A-invariant normal subgroup T of G containing HG such that G=HT and (H∩T)/HG is a p′-group, where HG is the core of H in G and p is a fixed prime dividing the order of G. Under the assumptions of some specific n-maximal A-invariant subgroups having ACp-normality, we establish several criteria for p-solvability of finite groups, where n∈{1,2,3}. Some earlier results in the literature were extended.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Operator Algebra Research
Geometric and Algebraic Topology
Publication details
- Journal / source
- Communications in Algebra
- Publisher
- Informa UK Limited
- Volume
- 54
- Issue
- 9
- Pages
- 3224–3232
- Publication date
- 5 January 2026
- Language
- EN