Minimal generation of transitive permutation groups

被引：5
作者：
Tracey, Gareth M. [1 ]
机构：
[1] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England
来源：
JOURNAL OF ALGEBRA | 2018年 / 509卷
基金：
英国工程与自然科学研究理事会;
关键词：
Group theory; Finite group theory; Permutation groups; Combinatorics; SUBGROUPS;
D O I：
10.1016/j.jalgebra.2018.04.030
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper discusses upper bounds on the minimal number of elements d(G) required to generate a transitive permutation group G, in terms of its degree n, and its order vertical bar G vertical bar. In particular, we reduce a conjecture of L. Pyber on the number of subgroups of the symmetric group Sym(n). We also prove that our bounds are best possible. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：40 / 100
页数：61
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