On finite totally k-closed groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914692988928000 |
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| author | He, Jiawei Li, Xiaogang |
| author_facet | He, Jiawei Li, Xiaogang |
| contents | Let $G$ be a finite group acting faithfully on a finite set $Ω$. For a positive integer $k$, $G$ acts naturally on the Catesian product $Ω^k := Ω\times ...\times Ω$. In this paper, we prove that finite nilpotent group $G$ with $2\nmid |G|$ is a totally $k$-closed group if and only if $G$ is abelian with $n(G)\leq k-1$ or cyclic, where $n(G)$ is the number of invariant factors in the invariant factor decomposition of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On finite totally k-closed groups He, Jiawei Li, Xiaogang Group Theory Combinatorics Let $G$ be a finite group acting faithfully on a finite set $Ω$. For a positive integer $k$, $G$ acts naturally on the Catesian product $Ω^k := Ω\times ...\times Ω$. In this paper, we prove that finite nilpotent group $G$ with $2\nmid |G|$ is a totally $k$-closed group if and only if $G$ is abelian with $n(G)\leq k-1$ or cyclic, where $n(G)$ is the number of invariant factors in the invariant factor decomposition of $G$. |
| title | On finite totally k-closed groups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2402.17240 |