Centralizers in pseudo-finite groups
Group Theory
2020-11-05 v3 Logic
Abstract
The role of finite centralizers of involutions in pseudo-finite groups is analyzed. It is shown that a pseudo-finite group admitting a definable involutory automorphism fixing only finitely many elements is finite-by-abelian-by-finite. As a consequence, we give a model-theoretic proof of a result for periodic groups due to Hartley and Meixner. Furthermore, it is shown that any pseudo-finite group has an infinite abelian subgroup.
Cite
@article{arxiv.1702.08173,
title = {Centralizers in pseudo-finite groups},
author = {Nadja Hempel and Daniel Palacin},
journal= {arXiv preprint arXiv:1702.08173},
year = {2020}
}