The purpose of the following considerations is to give a summary of the existing results on different questions connected with the maximal abelian subrings of factors of different types, mostly of type II. Their importance is explained through their role in group representation theory and, very probably, in the theory of factors of type II and III. The structure of the maximal abelian subrings of these factors, as revealed notably in the investigations of Dixmier, display fargoing differences when contrasted with those of factors of type I. In view of our very limited present knowledge about the algebraic structure of factors of type II and III the hope for an early explanation of the phenomena encountered below seems to be premature.
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