Virtually free pro-p products

TL;DR

The paper proves that finitely generated virtually free pro-p groups can be decomposed into free pro-p products with amalgamation or pro-p HNN-extensions over finite p-groups, generalizing earlier results.

Contribution

It extends the structure theory of finitely generated virtually free pro-p groups by showing their decomposition as fundamental groups of finite graphs of finitely generated pro-p groups.

Findings

G is a free pro-p product with amalgamation or HNN-extension over finite p-groups

G is the pro-p fundamental group of a finite graph of finitely generated pro-p groups

Generalizes previous structural results by Herfort and the second author

Abstract

It is shown that a finitely generated pro-p group G which is a virtually free pro-p product splits either as a free pro-p product with amalgamation or as a pro-p HNN-extension over a finite p-group. More precisely, G is the pro-p fundamental group of a finite graph of finitely generated pro-p groups with finite edge groups. This generalizes previous results of W. Herfort and the second author (cf. [2]).