Beauville p-groups of wild type and groups of maximal class

Gustavo A. Fernández-Alcober, Norberto Gavioli, Şükran Gül, Carlo M. Scoppola
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Abstract

Let G be a Beauville p-group. If G exhibits a ‘good behaviour’ with respect to taking powers, then every lift of a Beauville structure of \(G/\Phi (G)\) is a Beauville structure of G. We say that G is a Beauville p-group of wild type if this lifting property fails to hold. Our goal in this paper is twofold: firstly, we fully determine the Beauville groups within two large families of p-groups of maximal class, namely metabelian groups and groups with a maximal subgroup of class at most 2; secondly, as a consequence of the previous result, we obtain infinitely many Beauville p-groups of wild type.

野生型博维尔 p 群和最大类群
让 G 是一个波维尔 p 群。如果 G 在取幂方面表现出 "良好行为",那么 \(G/\Phi (G)\) 的博维尔结构的每一次提升都是 G 的博维尔结构。我们在本文中的目标有两个:首先,我们完全确定了最大类 p 群的两个大家族中的 Beauville 群,即元胞群和最大子群的类最多为 2 的群;其次,作为前面结果的一个后果,我们得到了无限多的野生型 Beauville p 群。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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