Symmetric cohomology of groups and Poincaré duality

Mariam Pirashvili, Teimuraz Pirashvili

Let $G$ be a finite group of order $n$ and let $M$ be a $G$-module. We construct groups $H_{\ast }^{\varkappa }(G,M)$ for which $H_k^{\varkappa }(G,M^{tw})\cong H_{\lambda }^{n-k-1}(G,M),$ where $M^{…