Gustavo A. Fernández-Alcober, Norberto Gavioli, Şükran Gül, Carlo M. Scoppola
{"title":"Beauville p-groups of wild type and groups of maximal class","authors":"Gustavo A. Fernández-Alcober, Norberto Gavioli, Şükran Gül, Carlo M. Scoppola","doi":"10.1007/s00605-024-01982-y","DOIUrl":null,"url":null,"abstract":"<p>Let <i>G</i> be a Beauville <i>p</i>-group. If <i>G</i> exhibits a ‘good behaviour’ with respect to taking powers, then every lift of a Beauville structure of <span>\\(G/\\Phi (G)\\)</span> is a Beauville structure of <i>G</i>. We say that <i>G</i> is a Beauville <i>p</i>-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 <i>p</i>-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 <i>p</i>-groups of wild type.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"50 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monatshefte für Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00605-024-01982-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.
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。