Subgroups of pro-p PD3-groups
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| Main Author: | |
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| Publication Date: | 2021 |
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| Format: | Article |
| Language: | eng |
| Source: | Repositório Institucional da UnB |
| Download full: | https://repositorio.unb.br/handle/10482/43782 https://doi.org/10.1007/s00605-020-01505-5 https://orcid.org/ 0000-0001-7418-7144 |
Summary: | 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. |
| Summary: | 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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