Finitely generated infinite torsion groups that are residually finite simple

TL;DR

This paper constructs finitely generated infinite torsion groups that are residually finite simple, answering a longstanding question and expanding understanding of the structure of such groups.

Contribution

It demonstrates the existence of finitely generated infinite torsion groups that are residually finite simple, a previously unresolved problem.

Findings

Existence of finitely generated infinite torsion groups that are residually finite simple

Embedding of residually finite torsion groups into finitely generated torsion simple groups

Provides a new class of groups with complex residual properties

Abstract

We show that every finitely generated residually finite torsion group $G$ embeds in a finitely generated torsion group $\Gamma$ that is residually finite simple. In particular we show the existence of finitely generated infinite torsion groups that are residually finite simple, which answers a question of Olshanskii and Osin.