Finite groups in which every proper characteristic subgroup is cyclic
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917275097890816 |
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| author | Damele, Marco Mastrogiacomo, Fabio |
| author_facet | Damele, Marco Mastrogiacomo, Fabio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03648 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite groups in which every proper characteristic subgroup is cyclic Damele, Marco Mastrogiacomo, Fabio Group Theory 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. |
| title | Finite groups in which every proper characteristic subgroup is cyclic |
| topic | Group Theory |
| url | https://arxiv.org/abs/2508.03648 |