Which integral group rings are Bass orders?
The group rings \({\hat {\mathbb{Z}}}_ pG\) over the complete ring \({\hat {\mathbb{Z}}}_ p\) of p-adic integers which are Bass orders are characterized as those for which G is a semidirect product of a \(p'\)-group by a p-group of order \(\leq p\). The proof is carried out by means of the classification of local Bass orders (Drozd, Kirichenko, Rojter) and \textit{S. A. Amitsur}'s work on finite subgroups of skewfields [Trans. Am. Math. Soc. 80, 361-386 (1955; Zbl 0065.256)]; it also implies that \({\hat {\mathbb{Z}}}_ pG\) is Bass if and only if its principal block is a Bass order. As a corollary, it follows that \({\mathbb{Z}}G\) is Bass if and only if G is cyclic of squarefree order.
scientific article; zbMATH DE number 4130578
scientific article