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20.118 (2022)

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Let $G$ be a pro-$p$ group that is a 3-dimensional Poincaré duality group. Can it contain a direct product $F_2 \times F_2$ of free pro-$p$ groups of rank 2?

If it can, then the answer to 20.117 is negative, but in the abstract case it is known that it can not (P. H. Kropholler, M. A. Roller, J. London Math. Soc. (2), 39 (1989), 271–284).

Contributor: P. Zalesskii

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