2017/01/25 by Fernández-Alcober, Gustavo A., Gavioli, Norberto, Gül, Şükran +1
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1701.07361
Let G be a Beauville finite 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.