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arXiv · 1810.00638

Infinitely Generated virtually free pro-$p$ groups and $p$-adic representations

Pavel Zalesskii
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Abstract

We prove the pro-$p$ version of the Karras, Pietrowski, Solitar, Cohen and Scott result stating that a virtually free group acts on a tree with finite vertex stabilizers. If a virtually free pro-$p$ group $G$ has finite centralizes of all non-trivial torsion elements more stronger statement is proved: $G$ embeds into a free pro-$p$ product of a free pro-$p$ group and finite $p$-group. The integral $p$-adic representation theory is used in the proof; it replaces the Stallings theory of ends in the pro-$p$ case.

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Pavel Zalesskii. 2018-10-04. Infinitely Generated virtually free pro-$p$ groups and $p$-adic representations. https://doi.org/10.1112/topo.12086

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