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arXiv · 1107.2331

On pro-$p$ analogues of limit groups via extensions of centralizers

Dessislava H. Kochloukova·Pavel A. Zalesskii
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Abstract

We begin a study of a pro-$p$ analogue of limit groups via extensions of centralizers and call $\mathcal{L}$ this new class of pro-$p$ groups. We show that the pro-$p$ groups of $\mathcal{L}$ have finite cohomological dimension, type $FP_{\infty}$ and non-positive Euler characteristic. Among the group theoretic properties it is proved that they are free-by-(torsion-free poly -procyclic) and if non-abelian do not have a finitely generated non-trivial normal subgroup of infinite index. Furthermore it is shown that every 2 generated pro-$p$ group in the class $\mathcal{L}$ is either free pro-$p$ or abelian.

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Dessislava H. Kochloukova, Pavel A. Zalesskii. 2011-07-12. On pro-$p$ analogues of limit groups via extensions of centralizers. https://arxiv.org/abs/1107.2331

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