Random graph products of finite groups are rational duality groups

TL;DR

This paper investigates the cohomological properties of random graph products of finite groups, showing that they are rational duality groups with high probability as the number of vertices grows.

Contribution

It establishes that random graph products of finite groups are rational duality groups with probability approaching one, extending to random right-angled Coxeter groups.

Findings

Random graph products are rational duality groups asymptotically almost surely.

Includes random right-angled Coxeter groups as a special case.

Provides new insights into the cohomology of random group constructions.

Abstract

Given an edge-independent random graph G(n,p), we determine various facts about the cohomology of graph products of groups for the graph G(n,p). In particular, the random graph product of a sequence of finite groups is a rational duality group with probability tending to 1 as n goes to infinity. This includes random right angled Coxeter groups as a special case.