On the isomorphism problem for monoids of product-one sequences

TL;DR

This paper proves that the monoids of product-one sequences over torsion groups are isomorphic if and only if the underlying groups are isomorphic, extending a known result from abelian to non-abelian groups.

Contribution

It generalizes the isomorphism characterization of monoids of product-one sequences from abelian to all torsion groups.

Findings

Monoids of product-one sequences over torsion groups are isomorphic iff the groups are isomorphic.

Extends previous results from abelian to non-abelian torsion groups.

Provides a complete characterization of monoid isomorphisms in this context.

Abstract

Let $G_1$ and $G_2$ be torsion groups. We prove that the monoids of product-one sequences over $G_1$ and over $G_2$ are isomorphic if and only if the groups $G_1$ and $G_2$ are isomorphic. This was known before for abelian groups.