Yarı direkt çarpımların kohomolojisi

Let ?=LG be a semidirect product where G is a finite cyclic group and L is a finitely generated ZG-lattice. Adem-Ge-Pan-Petrosyan [8] stated a conjecture which says that the cohomology of ? is given by the following isomorphism, . However, Langer-L uck [10] and later Petrosyan-Putrycz [9] showed that there are some groups which do not satisfy this isomorphism. In this thesis we do some explicit calculations related to this conjecture. Through the thesis we consider the case where dimL = 4. In fact, dimension 4 is the lowest dimension for L where the semidirect group ? = LG does not satisfy the conjecture. According to [9], in dimension 4 there are 44 nonisomorphic representations and only 2 of them do not satisfy the conjecture. We consider two of these 44 representations where one of them is counterexample for the conjecture of Adem-Ge-Pan-Petrosyan and the other one satises it. These results were already stated in [9]. In this thesis, we make detailed calculations for the cohomology of ? for these representations by using the method of N. Petrosyan and B. Putrycz.