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arXiv · 2511.16583

Finite simple groups have many classes of prime order elements

Jessica Anzanello·Pablo Spiga
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Abstract

Let $T$ be a finite non-abelian simple group. Giudici, Morgan and Praeger have shown that the order of $T$ is bounded above by a function depending on the maximum number of $\mathrm{Aut}(T)$-classes of elements of $T$ of prime-power order. In this note, we strengthen this result by showing, in particular, that prime-power can be replaced by prime.

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Jessica Anzanello, Pablo Spiga. 2025-11-20. Finite simple groups have many classes of prime order elements. https://arxiv.org/abs/2511.16583

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