Profinite genus of free products with finite amalgamation

2023/05/25 by Vagner R. de Bessa, de Bessa, Vagner R., Anderson L. P. Porto +3 · 1 citation
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2305.16054

openalex publication_date 2023/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A finitely generated residually finite group G is an \widehatOE-group if any action of its profinite completion \widehat G on a profinite tree with finite edge stabilizers admits a global fixed point. In this paper, we study the profinite genus of free products G₁*_HG₂ of \widehatOE-groups G₁,G₂ with finite amalgamation H. Given such G₁,G₂,H we give precise formulas for the number of isomorphism classes of G₁*_HG₂ and of its profinite completion. We compute the genus of G₁*_HG₂ and list various situations when the formula for the genus simplifies.

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