Geodesic
Group Rings over Z(p) with FC Unit Groups
Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1266-1269

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Let RG denote the group ring of a group G over a commutative ring R with unity. We recall that a group is said to be an FC-group if all its conjugacy classes are finite.In [6], S. K. Sehgal and H. Zassenhaus gave necessary and sufficient conditions for U(RG) to be an FC-group when R is either Z, the ring of rational integers, or a field of characteristic 0.One of the authors considered this problem for group rings over infinite fields of characteristic p ≠ 2 in [5] and G. Cliffs and S. K. Sehgal [1] completed the study for arbitrary fields. Also, group rings of finite groups over commutative rings containing Z(p ), a localization of Z over a prime ideal (p) were studied in [4]. 
Merklen, H.; Milies, C. Polcino. Group Rings over Z(p) with FC Unit Groups. Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1266-1269. doi: 10.4153/CJM-1980-095-8
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[7] 7. Zassenhaus, H. J., On the torsion units of finite group rings, in Studies in Mathematics (in honor of A. Almeida Costa), Instituto de Alta Cultura, Lisboa (1974). Google Scholar

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