Group cohomology

For a finite group G and its module M,

H^{0}(G,M) is isomorphic to M/Norm(M) where Norm(m) = \sum_{\sigma\in G}\sigma m

 

 

 

Alejandro Adem, Recent developments in the cohomology of finite groups, Notices Amer. Math. Soc. 44 (1997), no. 7, 806–812 http://www.ams.org/notices/199707/adem.pdf