Mixability of finite groups

TL;DR

This paper investigates the concept of mixability in finite groups, establishing conditions, obstructions, and demonstrating that many classes of groups, including simple and Coxeter groups, are mixable, along with bounds on mixing length.

Contribution

It introduces the concept of mixability in finite groups, providing criteria, identifying obstructions, and proving that various important classes of groups are mixable.

Findings

2-groups, symmetric groups, simple alternating groups are mixable

Bounds on the mixing length for these groups are provided

Most finite Coxeter groups are also shown to be mixable

Abstract

Say that a finite group $G$ is mixable if a product of random elements, each chosen independently from two options, can distribute uniformly on $G$. We present conditions and obstructions to mixability. We show that $2$-groups, the symmetric groups, the simple alternating groups, several matrix and sporadic simple groups, and most finite Coxeter groups, are mixable. We also provide bounds on the mixing length of such groups.