On the generalized Fitting height and insoluble length of finite groups
Group Theory
2020-06-24 v3
Abstract
We prove two conjectures of E. Khukhro and P. Shumyatsky concerning the Fitting height and insoluble length of finite groups. As a by-product of our methods, we also prove a generalization of a result of Flavell, which itself generalizes Wielandt's Zipper Lemma and provides a characterization of subgroups contained in a unique maximal subgroup. We also derive a number of consequences of our theorems, including some applications to the set of odd order elements of a finite group inverted by an involutory automorphism.
Keywords
Cite
@article{arxiv.1910.04692,
title = {On the generalized Fitting height and insoluble length of finite groups},
author = {Robert M. Guralnick and Gareth Tracey},
journal= {arXiv preprint arXiv:1910.04692},
year = {2020}
}