Geodesic
Class groups and automorphism groups of group rings
Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 79-86

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This paper is a sequel to [2]. A polycyclic-by-finite group G was there called dihedral free if G contains no subgroup isomorphic to 〈b, a:ba = b-1 a2 = 1〉 whose normalizer has finite index in G. It was shown in [2, Theorem F] that, if R is a commutative Noetherian domain, the group ring RG is a prime Noetherian maximal order if and only if R is integrally closed, G is dihedral free, and G has no non-trivial finite normal subgroups. Throughout, R and G will be assumed to satisfy these hypotheses. The main aim of the paper is to study the class group of the maximal order RG. 
Brown, Kenneth A. Class groups and automorphism groups of group rings. Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 79-86. doi: 10.1017/S0017089500006376
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