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.

中文翻译：

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pro-p $$PD ^3$$-groups 的子组

我们本着 Robert Bieri 和 Jonathan Hillmann 的工作精神研究了 3 维 Poincaré 对偶性 p 群，并表明如果这样的 p 群 G 有一个非平凡的有限呈现的无穷指数次正规子群，那么子群是循环且正规的或子群是循环的且群是多环的，或子群是 Demushkin 且在 G 的开子群中是正规的。此外，我们描述了 3 维庞加莱对偶属性群的有限生成子群的中心化子。