Unit groups of semisimple group algebras of Abelian \(p\)-groups over a field (Q1355529)

Let \(G\) be an abelian \(p\)-group, \(K\) a field of characteristic different from \(p\) and let \(KG\) be the group algebra of \(G\) over \(K\). The authors give a description of the unit group \(U(KG)\) of \(KG\) when \(K\) is a field of the first kind with respect to \(p\) and the first Ulm factor \(G/G^1\) is a direct sum of cyclic groups, or when \(G\) is an arbitrary abelian \(p\)-group, and \(K\) is a field of the second kind with respect to \(p\). The indicated description of \(U(KG)\) extends results of \textit{Z. Chatzidakis} and \textit{P. Pappas} [J. Lond. Math. Soc., II. Ser. 44, No. 1, 9-23 (1991; Zbl 0701.16031)].