Abstract
We study 3-dimensional Poincaré 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 Poincaré duality pro-p groups.
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Communicated by Adrian Constantin.
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The second author is partially supported by FAPDF and CNPq. The paper was started when the second author was visiting the University of Milano-Biccoca and he thanks the Department of Mathematics of it for hospitality.
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Castellano, I., Zalesskii, P. Subgroups of pro-p \(PD ^3\)-groups. Monatsh Math 195, 391–400 (2021). https://doi.org/10.1007/s00605-020-01505-5
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DOI: https://doi.org/10.1007/s00605-020-01505-5