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arXiv · 2305.16054

Profinite genus of free products with finite amalgamation

Vagner R. de Bessa·Anderson L. P. Porto·Pavel A. Zalesskii
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Abstract

A finitely generated residually finite group $G$ is an $\widehat{OE}$-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 $G_1*_HG_2$ of $\widehat{OE}$-groups $G_1,G_2$ with finite amalgamation $H$. Given such $G_1,G_2,H$ we give precise formulas for the number of isomorphism classes of $G_1*_HG_2$ and of its profinite completion. We compute the genus of $G_1*_HG_2$ and list various situations when the formula for the genus simplifies.

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Vagner R. de Bessa, Anderson L. P. Porto, Pavel A. Zalesskii. 2023-05-25. Profinite genus of free products with finite amalgamation. https://arxiv.org/abs/2305.16054

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