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arXiv · 2609.01234

On commensurations of pro-$\mathcal{C}$ groups

Pedro Cusinato
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Abstract

We study commensurations of pro-$\mathcal{C}$ groups, where $\mathcal{C}$ is an extension-closed variety of finite groups. We characterize those commensurations of pro-$\mathcal{C}$ groups that can be extended to embeddings into a common overgroup, obtaining a pro-$\mathcal{C}$ analog of a recent theorem by Touikan. We also consider obtain a structural result on virtual retracts of pro-$\mathcal{C}$ groups.

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Pedro Cusinato. 2026-09-01. On commensurations of pro-$\mathcal{C}$ groups. https://arxiv.org/abs/2609.01234

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