Strongly generating elements in finite and profinite groups

Published 11 Aug 2022 in math.GR | (2208.05761v1)

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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