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.
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页码：40 / 100
页数：61
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