Units in modular group algebra

Abstract

Let U(FG) denotes the unit group of FG. In this article, we compute the order of U(F(G ⋉ C2 n )) in terms of the order of U(FG) for an arbitrary nite group G, where C2 n is the cyclic group of order 2n and F is a nite eld of characteristic 2. Further, if A is an elementary abelian 2-group, then we obtain structures of U(F(G × A)) and its unitary subgroup U∗(F(G × A)), where ∗ is the canonical involution of the group algebra F(G × A). Finally, we provide a set of generators of U∗(FD4m) and U(FD4m). AR