Large minimal invariable generating sets in the finite symmetric groups

Daniele Garzoni; Nick Gill

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arXiv · 2012.08815

Large minimal invariable generating sets in the finite symmetric groups

Daniele Garzoni·Nick Gill

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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 $n\rightarrow \infty$.

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Daniele Garzoni, Nick Gill. 2020-12-16. Large minimal invariable generating sets in the finite symmetric groups. https://arxiv.org/abs/2012.08815

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