Geodesic
On Class Sums in p-Adic Group Rings
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 541-543

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we prove that an isomorphism of p-adic group rings of finite p-groups maps class sums onto class sums. For integral group rings this is a well known theorem of Glauberman (see [3; 7]). As an application, we show that any automorphism of the p-adic group ring of a finite p-group of nilpotency class 2 is composed of a group automorphism and a conjugation by a suitable element of the p-adic group algebra. This was proved for integral group rings of finite nilpotent groups of class 2 in [5]. In general this question remains open. We also indicate an extension of a theorem of Passman and Whitcomb. The following notation is used. G denotes a finite p-group. Z denotes the ring of (rational) integers. ZP denotes the ring of p-adic integers. Qp denotes the p-adic number field. 
Sehgal, Sudarshan K. On Class Sums in p-Adic Group Rings. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 541-543. doi: 10.4153/CJM-1971-058-5
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