Minimal invariable generating sets

Daniele Garzoni; Andrea Lucchini

Minimal invariable generating sets

Group Theory 2022-03-03 v1

Authors: Daniele Garzoni , Andrea Lucchini

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.

Keywords

finite group theory additive combinatorics group theory

Cite

@article{arxiv.2203.00726,
  title  = {Minimal invariable generating sets},
  author = {Daniele Garzoni and Andrea Lucchini},
  journal= {arXiv preprint arXiv:2203.00726},
  year   = {2022}
}

Comments

This is a belated posting of a 2019 paper. 24 pp

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