Maximal subgroups of small index of finite almost simple groups

被引：1

作者：

Ballester-Bolinches, Adolfo ^{[1
]}

Esteban-Romero, Ramon ^{[1
]}

Jimenez-Seral, Paz ^{[2
]}

机构：

[1] Univ Valencia, Dept Matemat, Dr Moliner 50, Valencia 46100, Spain

[2] Univ Zaragoza, Dept Matemat, Pedro Cerbuna 12, Zaragoza 50009, Spain

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2022年 / 116卷 / 04期

关键词：

Finite group; Maximal subgroup; Simple group; Almost simple group; MONSTER;

D O I：

10.1007/s13398-022-01327-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove in this paper that every almost simple group R with socle isomorphic to a simple group S possesses a conjugacy class of core-free maximal subgroups whose index coincides with the smallest index 1(S) of a maximal subgroup of S or a conjugacy class of core-free maximal subgroups with a fixed index v(S) <= 1(S)(2), depending only on S. We also prove that the number of subgroups of the outer automorphism group of S is bounded by log(3) 1(S) and 1(S)(2) < vertical bar S vertical bar.

引用

页数：18

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022, 116
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