Author:
LUCCHINI ANDREA,MARION CLAUDE,TRACEY GARETH
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.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Prefrattini subgroups and crowns;Archiv der Mathematik;2023-06-12