Units in modular group algebra

摘要

Let U(FG) denotes the unit group of FG In this article, we compute the order of U(F(G x C(2)n)) terms'of the order of U(FG) for an arbitrary finite group G, where C(2)n is the cyclic group of order 2(n) and F is a finite field characteristic 2. Further, if A is an elementary abelian 2 -group, then we obtain structures of U(F(G x A)) and its unitary subgroup U-*(F(G x A)), where * is he canonical involution of the group algebra F(G x A) Finally, we Provide a set of generators of U-*(FD4m) and U(FD4m).