Some special coprime actions and their consequences
Journal of Pure and Applied Algebra, vol.228, no.12, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 228 Issue: 12
- Publication Date: 2024
- Doi Number: 10.1016/j.jpaa.2024.107764
- Journal Name: Journal of Pure and Applied Algebra
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
- Keywords: Coprime action, Fitting series, Frobenius action, p-length, Simple group
- Middle East Technical University Affiliated: Yes
Abstract
Let a group A act on the group G coprimely. Suppose that the order of the fixed point subgroup CG(A) is not divisible by an arbitrary but fixed prime p. In the present paper we determine bounds for the p-length of the group G in terms of the order of A, and investigate how some A-invariant p-subgroups are embedded in G under various additional assumptions.