In 1972 K.I.Tahara [7,2 Theorem 2.2.5] , using cohomological method, showed that if a finite group $G=T\\rhd\\!\\!\\!

In 1972 K.I.Tahara [7,2 Theorem 2.2.5] , using cohomological method, showed that if a finite group $G=T\\rhd\\!\\!\\! <N$ is the semidirect product of a normal subgroup $N$ and a subgroup $T$ , then $M(T)$ is a direct factor of $M(G)$ , where $M(G)$ is the Schur-multiplicator of $G$ and in the finite case , is the second cohomology group of $G$ . In 1977 W.Haebich [1 Theorem 1.7] gave another proof using a different method for an arbitrary group $G$ . In this paper we generalize the above theorem . We will show that ${\\cal N}_cM(T)$ is a direct factor of ${\\cal N}_cM(G)$ , where ${\\cal N}_c$ [3 page 102] is the variety of nilpotent groups of class at most $c\\geq 1$ and ${\\cal N}_cM(G)$ is {\\it the Baer-invariant} of the group $G$ with respect to the variety ${\\cal N}_c$ [3 page 107] .

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