Profinite properties of residually free groups

2023/06/22 by Morales, Ismael
#20E18 #20E26 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2306.13082

Abstract

Henry Wilton classified when a prime three-manifold M has a residually free fundamental group π₁ M. We prove that the groups π₁ M× \mathbb Zⁿ are profinitely rigid within finitely generated residually free groups. We also establish other profinite invariants of the class of residually free groups such as coherence and subgroup separability. In the course of our proofs, we generalise a lemma of Wilton and Zalesskii on profinitely recognising when a central extension of groups splits.

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