On pro-$p$ analogues of limit groups via extensions of centralizers
Abstract
We begin a study of a pro- analogue of limit groups via extensions of centralizers and call this new class of pro- groups. We show that the pro- groups of have finite cohomological dimension, type 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- group in the class is either free pro- or abelian.
Keywords
Cite
@article{arxiv.1107.2331,
title = {On pro-$p$ analogues of limit groups via extensions of centralizers},
author = {Dessislava H. Kochloukova and Pavel A. Zalesskii},
journal= {arXiv preprint arXiv:1107.2331},
year = {2011}
}
Comments
This is a correted version of the paper published in Math. Z. 267 (2011), no. 1-2, 109-128. The difference is Section 4, where we show that the proof of Theorem 4.1 of the published version proves that a pro-p limit group is free-by-(torsion free polyprocyclic). It does not however proves that a pro-p limit group is free-by-(torsion free finitely generated nilpotent)