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.
Beauville p-groups of wild type and groups of maximal class
Gavioli, Norberto;Scoppola, Carlo M.
2024-01-01
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.File in questo prodotto:
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