Abstract:
Let p be an odd prime, D2p be the dihedral group of order 2p, and F2 be the finite field with two elements. If * denotes the canonical involution of the group algebra F2D2p, then bicyclic units are unitary units. In this note, we investigate the structure of the ℬ(F2D2p), generated by the bicyclic units of the group algebra F2D2p. Further, we obtain the structure of the unit group U(F2D2p) and the unitary subgroup U *(F2D2p), and we prove that both ℬ(F2D2p) and U*(F2D 2p) are normal subgroups of U(F2D2p).
