具有小多重全纯型的第二类的有限𝑝-groups

Pub Date : 2023-09-06 DOI:10.1515/jgth-2023-0054

A. Caranti, Cindy (Sin Yi) Tsang

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引用次数: 0

摘要

摘要利用二阶有限的𝑝-group𝐺对奇数素数𝑝的纯态，考虑了多重纯态的商群T¹(G) T(G)。通过第一作者的工作，我们知道T(G) T(G)包含一个p r−1 (p−1)p^{r-1}(p-1)阶的循环子群，其中p r p^{r}是𝐺的商的中心的指数。在本文中，我们将展示𝐺(r=1 r=1)的例子，使得T¹(G) T(G)的阶恰好是p−1 p-1，这是尽可能小的。

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

Abstract We consider the quotient group T ⁢ ( G ) 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 ) T(G) contains a cyclic subgroup of order p r − 1 ⁢ ( p − 1 ) p^{r-1}(p-1) , where p r 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 r=1 ) such that T ⁢ ( G ) T(G) has order exactly p − 1 p-1 , which is as small as possible.

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