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Integral Group Rings of Finite Groups

Published online by Cambridge University Press:  20 November 2018

B. Banaschewski
B. Banaschewski*
Affiliation:
Tulane University, New Orleans and McMaster University Hamilton, Ontario
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The main object of this paper is to show that the existence of a particular kind of isomorphism between the integral group rings of two finite groups implies that the groups themselves are isomorphic. The proof employs certain types of linear forms which are first discussed in general. These linear forms are in some way related to the bilinear forms used by Weidmann [3] in showing that groups with isomorphic character rings have the same character table, and a shorter and, in a sense, more natural proof of this result is included here as another application of these linear forms.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 5 , December 1967 , pp. 635 - 642
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras. Interscience Publishers, New York, 1962.Google Scholar
2. Higman, G., The units of group rings. Proc. London Math. Soc. 46 (1944), 231-248.Google Scholar
3. Weidman, D. R., The character ring of a finite group. 111. J. Math. 9 (1966), 462-467.Google Scholar