Year: 2025
Type: article
Abstract: It is proved that if a finite group has an automorphism of order with fixed points, then has a soluble subgroup whose index and Fitting height are bounded in terms of and . As a corollary, a problem of B. Hartley is solved in the affirmative: if a locally finite group has an element with finite centralizer, then has a subgroup of finite index which has a finite normal series with locally nilpotent factors.
DOI: 10.1112/blms.70206
Author: Evgeny Khukhro
Institution: University of Lincoln
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414649202