What does this research mean for the field?

There is a definitive list of all non-abelian finite simple groups that act with low fixity on one of their conjugacy classes, along with specific conditions under which the subgroup generated by the fixed point set is abelian. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to classify non-abelian finite simple groups that exhibit low fixity on their conjugacy classes.

May 16, 2026Open Access

Finite simple groups that act with low fixity on a conjugacy class

Key Points

This research aims to classify non-abelian finite simple groups that exhibit low fixity on their conjugacy classes.
Listed all non-abelian finite simple groups with low fixity on conjugacy classes.
Analyzed the fixed point set and its generated subgroups for abelian properties.
Identified specific groups demonstrating low fixity behavior.
Described conditions under which the generated subgroup is abelian.

Abstract

Abstract In this article, we list all possibilities for non-abelian finite simple groups that act with low fixity on one of their conjugacy classes, and we give information about when the subgroup generated by the fixed point set is abelian.

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Cite This Study

Möller et al. (Thu,) studied this question.

synapsesocial.com/papers/6a080a29a487c87a6a40c100 https://doi.org/https://doi.org/10.1007/s00013-026-02241-2

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