Finite groups in which every proper characteristic subgroup is cyclic
Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Damele, Marco, Mastrogiacomo, Fabio
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7077052227
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