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

Ilaria Castellano; Pavel Zalesskii

doi:10.1007/s00605-020-01505-5

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arXiv · 2005.00423

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

Ilaria Castellano·Pavel Zalesskii

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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.

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BibTeX RIS

Ilaria Castellano, Pavel Zalesskii. 2020-05-01. Subgroups of pro-$p$ $\mathrm{PD}^3$-groups. https://doi.org/10.1007/s00605-020-01505-5

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