Large minimal invariable generating sets in the finite symmetric groups

Daniele Garzoni; Nick Gill

Large minimal invariable generating sets in the finite symmetric groups

Group Theory 2020-12-17 v1

Authors: Daniele Garzoni , Nick Gill

Abstract

For a finite group $G$ , let $m_I(G)$ denote the largest possible cardinality of a minimal invariable generating set of $G$ . We prove an upper and a lower bound for $m_I(S_n)$ , which show in particular that $m_I(S_n)$ is asymptotic to $n/2$ as $n\rightarrow \infty$ .

Keywords

combinatorial group theory group theory finite group theory

Cite

@article{arxiv.2012.08815,
  title  = {Large minimal invariable generating sets in the finite symmetric groups},
  author = {Daniele Garzoni and Nick Gill},
  journal= {arXiv preprint arXiv:2012.08815},
  year   = {2020}
}

Comments

12 pages

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