Metabelian thin Beauville $p$-groups

TL;DR

This paper characterizes Beauville structures within a specific class of metabelian thin p-groups, expanding understanding of their algebraic properties and potential applications.

Contribution

It identifies and classifies Beauville structures in metabelian thin p-groups, a previously unexplored class of groups.

Findings

Determined conditions for Beauville structures in these groups

Classified all such structures within the class

Enhanced understanding of thin p-group properties

Abstract

A non-cyclic finite $p$-group $G$ is said to be thin if every normal subgroup of $G$ lies between two consecutive terms of the lower central series and $|\gamma_i(G):\gamma_{i+1}(G)|\le p^2$ for all $i\geq 1$. In this paper, we determine Beauville structures in metabelian thin $p$-groups.