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


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Fernández-Alcober G. A., Gavioli N., Gül Erdem Ş., Scoppola C. M.

Monatshefte fur Mathematik, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2024
  • Doi Number: 10.1007/s00605-024-01982-y
  • Journal Name: Monatshefte fur Mathematik
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: 14J29, 20D15, Beauville p-groups, p-Groups of maximal class
  • TED University Affiliated: Yes

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/Φ(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.