Homological growth of nilpotent-by-abelian pro-p groups

Dessislava H. Kochloukova; Aline G. S. Pinto

Homological growth of nilpotent-by-abelian pro-p groups

Group Theory 2025-10-02 v1

Authors: Dessislava H. Kochloukova , Aline G. S. Pinto

Abstract

We show that the torsion-free rank of $H_i(M, \mathbb{Z}_p)$ has finite upper bound for $i \leq m$ , where $M$ runs through the pro- $p$ subgroups of finite index in a pro- $p$ group $G$ that is (nilpotent of class $c$ )-by-abelian such that $G/N'$ is of type $FP_{2cm}$ .

Keywords

nilpotent groups pro-p groups homological growth torsion-free rank FP groups

Cite

@article{arxiv.2510.00421,
  title  = {Homological growth of nilpotent-by-abelian pro-p groups},
  author = {Dessislava H. Kochloukova and Aline G. S. Pinto},
  journal= {arXiv preprint arXiv:2510.00421},
  year   = {2025}
}

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