arXiv Open Access 2023

Finite $p$-groups of class two with a small multiple holomorph

A. Caranti Cindy Tsang

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Abstrak

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.

Topik & Kata Kunci

math.GR

Penulis (2)

A. Caranti

Cindy Tsang

Format Sitasi

APA MLA BibTeX

Caranti, A., Tsang, C. (2023). Finite $p$-groups of class two with a small multiple holomorph. https://arxiv.org/abs/2303.10638

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓