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Let $G$ be a finite group, and let $M$ be a finitely generated $G$-module, that is, a finitely generated abelian group on which $G$ acts. We work with the first homology group $$ H_1(G,M).$$ For any ...

Let $G$ be a finite group and $M$ be a finitely generated $G$-module, that is, a finitely generated abelian group on which $G$ acts. Consider the functor $$ (G,M)\rightsquigarrow F(G,M):= (M_G)_{\rm ...

Let $G$ be a finite group. Let $M$ be a finite $G$-module (a finite abelian group with an action of $G$). We consider a special kind of $G$-modules; in particular, our $M$ is a finite dimensional ...