Generating maximal subgroups of finite almost simple groups
| Autor: | Lucchini, Andrea, Marion, Claude, Tracey, Gareth |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Forum of Mathematics, Sigma 8 (2020) e32 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/fms.2019.43 |
| Popis: | For a finite group $G$, let $d(G)$ denote the minimal number of elements required to generate $G$. In this paper, given a finite almost simple group $G$ and any maximal subgroup $H$ of $G$, we determine a precise upper bound for $d(H)$. In particular, we show that $d(H)\leq 5$, and that $d(H)\geq 4$ 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. |
| Databáze: | arXiv |
| Externí odkaz: |
|