Finite $p$-groups of class two with a small multiple holomorph
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914698704715776 |
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| author | Caranti, A. Tsang, Cindy |
| author_facet | Caranti, A. Tsang, Cindy |
| contents | We consider the quotient group $T(G)$ of the multiple holomorph by the holomorph of a finite $p$-group $G$ of class two for an odd prime $p$. By work of the first-named author, we know that $T(G)$ contains a cyclic subgroup of order $p^{r-1}(p-1)$, where $p^r$ is the exponent of the quotient of $G$ by its center. In this paper, we shall exhibit examples of $G$ (with $r = 1$) such that $T(G)$ has order exactly $p-1$, which is as small as possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10638 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite $p$-groups of class two with a small multiple holomorph Caranti, A. Tsang, Cindy Group Theory 20B35 20D15 20D45 We consider the quotient group $T(G)$ of the multiple holomorph by the holomorph of a finite $p$-group $G$ of class two for an odd prime $p$. By work of the first-named author, we know that $T(G)$ contains a cyclic subgroup of order $p^{r-1}(p-1)$, where $p^r$ is the exponent of the quotient of $G$ by its center. In this paper, we shall exhibit examples of $G$ (with $r = 1$) such that $T(G)$ has order exactly $p-1$, which is as small as possible. |
| title | Finite $p$-groups of class two with a small multiple holomorph |
| topic | Group Theory 20B35 20D15 20D45 |
| url | https://arxiv.org/abs/2303.10638 |