Cohomology of groups

Abstract

let G be a group and ZG be its integral group ring. Thus an additive group ZG is the free abelian group with the element of G, a ZG Module M is the same thing as specifying an abelian group M on which G acts,  An abelian group Hⁿ (G, M) where n= 0,1,2,3…… called Cohomology of G with the coefficients in the  ZG - module M. In this paper we explore the notion of Cohomology of finite groups and infinite groups.