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arXiv · 2208.05761

Strongly generating elements in finite and profinite groups

Eloisa Detomi·Andrea Lucchini
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Abstract

Given a finite group $G$ and an element $g\in G$, we may compare the expected number $e(G)$ of elements needed to generate $G$ and the expected number $e(G,g)$ of elements of $G$ needed to generate $G$ together with $g.$ We address the following question: how large can the difference $e(G)-e(G,g)$ be?

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Eloisa Detomi, Andrea Lucchini. 2022-08-11. Strongly generating elements in finite and profinite groups. https://arxiv.org/abs/2208.05761

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