Article contents
GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS
Published online by Cambridge University Press: 30 June 2020
Abstract
For a finite group $G$, let
$d(G)$ denote the minimal number of elements required to generate
$G$. In this paper, we prove sharp upper bounds on
$d(H)$ whenever
$H$ is a maximal subgroup of a finite almost simple group. In particular, we show that
$d(H)\leqslant 5$ and that
$d(H)\geqslant 4$ if and only if
$H$ occurs in a known list. This improves a result of Burness, Liebeck and Shalev. The method involves the theory of crowns in finite groups.
MSC classification
- Type
- Algebra
- Information
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Copyright
- © The Author(s) 2020
References
- 1
- Cited by