As we will see in Section IX, the isomorphism problem is closely related to the study of augmentation preserving automorphisms of the group ring (cf. the discussion of the Zassenhaus conjecture in [R-S; 87 3]), and to the structure of the group of augmented units in the group ring. We shall quote here without proof the most far reaching result, which has been obtained so far (cf. [Sc; 87] and [Sc; 90]).
KeywordsCommutative Diagram Direct Summand Group Ring Splitting Field Isomorphism Problem
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