Subgroups of pro-$p$ $\mathrm{PD}^3$-groups

DOI10.1007/S00605-020-01505-5arXiv2005.00423MaRDI QIDQ6339831

Pavel A. Zalesskii, I. Castellano

Publication date: 1 May 2020

Abstract: We study 3-dimensional Poincar'e duality pro-$p$ groups in the spirit of the work by Robert Bieri and Jonathan Hillmann, and show that if such a pro-$p$ group $G$ has a nontrivial finitely presented subnormal subgroup of infinite index, then either the subgroup is cyclic and normal, or the subgroup is cyclic and the group is polycyclic, or the subgroup is Demushkin and normal in an open subgroup of $G$. Also, we describe the centralizers of finitely generated subgroups of 3-dimensional Poincar'e duality pro-$p$ groups.

Mathematics Subject Classification ID

Limits, profinite groups (20E18)

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