Conjugate generation of sporadic almost simple groups

Danila O. Revin; Andrei V. Zavarnitsine

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arXiv · 2505.05173

Conjugate generation of sporadic almost simple groups

Danila O. Revin·Andrei V. Zavarnitsine

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Abstract

As defined by Guralnick and Saxl, given a nonabelian simple group $S$ and its nonidentity automorphism $x$, a natural number $\alpha_S(x)$ is the minimum number of conjugates of $x$ in $\langle x,S\rangle$ that generate a subgroup containing $S$. In this paper, for every sporadic group $S$ other than the Monster and an automorphism $x$ of $S$ of prime order, we complete the determination of the precise value of $\alpha_S(x)$.

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Danila O. Revin, Andrei V. Zavarnitsine. 2025-05-08. Conjugate generation of sporadic almost simple groups. https://arxiv.org/abs/2505.05173

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