Unit Groups of Semisimple Group Algebras of Abelianp-Groups over a Field, Original Research Article

LetGbe an abelianp-group, letKbe a field of characteristic different fromp, and letKGbe the group algebra ofGoverK. In this paper we give a description of the unit groupU(KG) ofKGwhen (i)Kis a field of the first kind with respect topand the first Ulm factorG/G1is a direct sum of cyclic groups and when (ii)Gis an arbitrary abelianp-group andKis a field of the second kind with respect top. The indicated description ofU(KG) extends results of[4].