Abstract
This paper reports on my talk The Group Ring Problem for Non-soluble Groups. Instead of being a transcription, it is a detailed elaboration on that aspect of the talk most accessible to ring theorists, a new proof of the fact that the integral group ring of a finite group determines the sizes of the conjugacy classes of the group. The proof is based on two themes which Akira Hattori emphasised in his studies in the isomorphism problem for group rings. The first is positive involutions of real group algebras applied to the involution defined on a normalised group basis by inversion. The second is the transition matrix from one such basis to another.
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© 1988 Springer-Verlag
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Sandling, R. (1988). A proof of the class sum correspondence using the real group algebra. In: Bueso, J.L., Jara, P., Torrecillas, B. (eds) Ring Theory. Lecture Notes in Mathematics, vol 1328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100929
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DOI: https://doi.org/10.1007/BFb0100929
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