1. Minimal invariable generating sets
- Author
-
Daniele Garzoni and Andrea Lucchini
- Subjects
Finite group ,Algebra and Number Theory ,Group (mathematics) ,010102 general mathematics ,Group Theory (math.GR) ,01 natural sciences ,Combinatorics ,Set (abstract data type) ,0103 physical sciences ,Generating set of a group ,FOS: Mathematics ,010307 mathematical physics ,0101 mathematics ,Element (category theory) ,Mathematics - Group Theory ,20F05, 20D99 ,Mathematics ,Conjugate - 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., This is a belated posting of a 2019 paper. 24 pp
- Published
- 2022