A Decomposition for the Low Dimensional Cohomology of Semidirect Product of Topological Groups

Abstract

Let $G$ be a topological group and $A$ a trivial $G$-module. Suppose $G$ is the semidirect product of a closed normal subgroup $N$ and   a subgroup $T$. In this paper we find, $H^i (G,A) ~ i=1,2$, the first and the second cohomology of $G$  in terms of its factors.