On finite groups in which the twisted conjugacy classes of the unit element are subgroups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913350371246080 |
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| author | Nicotera, Chiara |
| author_facet | Nicotera, Chiara |
| contents | We consider groups $G$ such that the set $[G,φ]=\{g^{-1}g^φ|g\in G\}$ is a subgroup for every automorphism $φ$ of $G$, and we prove that there exists such a group $G$ that is finite and nilpotent of class $n$ for every $n\in\mathbb N$. Then there exists an infinite nonnilpotent group with the above property and the conjecture 18.14 of $[5]$ is false. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On finite groups in which the twisted conjugacy classes of the unit element are subgroups Nicotera, Chiara Group Theory 20D15, 20D45, 20E45 We consider groups $G$ such that the set $[G,φ]=\{g^{-1}g^φ|g\in G\}$ is a subgroup for every automorphism $φ$ of $G$, and we prove that there exists such a group $G$ that is finite and nilpotent of class $n$ for every $n\in\mathbb N$. Then there exists an infinite nonnilpotent group with the above property and the conjecture 18.14 of $[5]$ is false. |
| title | On finite groups in which the twisted conjugacy classes of the unit element are subgroups |
| topic | Group Theory 20D15, 20D45, 20E45 |
| url | https://arxiv.org/abs/2405.08433 |