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arXiv · 2501.17806

Mixability of finite groups

Gideon Amir·Guy Blachar·Subhajit Ghosh·Uzi Vishne
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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.

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Gideon Amir, Guy Blachar, Subhajit Ghosh, Uzi Vishne. 2025-01-29. Mixability of finite groups. https://arxiv.org/abs/2501.17806

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