Series of $p$-groups with Beauville structure

TL;DR

The paper constructs infinite projective systems of finite p-groups with Beauville structures and introduces the concept of topological Beauville structures on pro-finite groups, providing new examples for p ≥ 5.

Contribution

It establishes the existence of infinite systems of p-groups with Beauville structures and introduces the notion of topological Beauville structures on pro-finite groups, with explicit examples for p ≥ 5.

Findings

Finite p-groups with Beauville structures form surjective systems.

Introduction of unmixed topological Beauville structures on pro-finite groups.

Explicit infinite series of non-abelian p-groups with Beauville structures for p ≥ 5.

Abstract

For every $p\geq 2$ we show that each finite $p$-group with an unmixed Beauville structure is part of a surjective infinite projective system of finite $p$-groups with compatible unmixed Beauville structures. This leads to the new notion of an unmixed topological Beauville structure on pro-finite groups. We further construct for $p \geq 5$ a new explicit infinite series of non-abelian $p$-groups that allow unmixed Beauville structures.