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arXiv · 2508.03648

Finite groups in which every proper characteristic subgroup is cyclic

Marco Damele·Fabio Mastrogiacomo
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Abstract

Let $G$ be a finite non-cyclic, non-characteristically simple group with the property that all proper characteristic subgroups of $G$ are cyclic. We call such a group $\mathrm{CCS}$ group, short for \emph{Characteristic Cyclic}. In this paper, we provide a complete classification of these groups. As an application of our main result, we also make some progress toward the classification of minimal non-cyclic skew braces.

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Marco Damele, Fabio Mastrogiacomo. 2025-08-05. Finite groups in which every proper characteristic subgroup is cyclic. https://arxiv.org/abs/2508.03648

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