Minimal invariable generating sets

2022/03/01 by Garzoni, Daniele, Lucchini, Andrea
#20D99 #20F05 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2203.00726

Abstract

A subset S of a group G invariably generates G if, when each element of S is replaced by an arbitrary conjugate, the resulting set generates G. An invariable generating set X of G is called minimal if no proper subset of X invariably generates G. We will address several questions related to the behaviour of minimal invariable generating sets of a finite group.

Related

• Invariable generation and the chebotarev invariant of a finite group
• Invariable generation and wreath products
• Invariable generation of certain branch groups
• Invariable Generation of Infinite Groups
• Large minimal invariable generating sets in the finite symmetric groups