On groups with all subgroups subnormal or soluble of bounded derived length
Group Theory
2015-04-02 v1
Abstract
In this paper, we deal with locally graded groups whose subgroups are either subnormal or soluble of bounded derived length, say d. In particular, we prove that every locally (soluble-by-finite) group with this property is either soluble or an extension of a soluble group of derived length at most d by a finite group, which fits between a minimal simple group and its automorphism group. We also classify all the finite non-abelian simple groups whose proper subgroups are metabelian.
Cite
@article{arxiv.1208.5617,
title = {On groups with all subgroups subnormal or soluble of bounded derived length},
author = {Kivanc Ersoy and Antonio Tortora and Maria Tota},
journal= {arXiv preprint arXiv:1208.5617},
year = {2015}
}