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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An invariant ideal of a group ring of a finite group. II


Authors: J. S. Hsia and Roger D. Peterson
Journal: Proc. Amer. Math. Soc. 51 (1975), 275-281
MSC: Primary 20C05
DOI: https://doi.org/10.1090/S0002-9939-1975-0384909-9
MathSciNet review: 0384909
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Abstract: The vanishing of the numerical invariant $ \nu (G)$ of a finite group $ G$ is linked to the existence of certain central annihilators of the generic right ideal $ {\Gamma _R}(G)$ in the group ring $ RG$. This leads to several affirmative answers of questions posed in [1]. Also, some explicit values of $ \nu (G)$ are described for the class of finite nonsolvable groups having all their odd Sylow subgroups cyclic.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0384909-9
Keywords: Invariant ideal of a group ring, numerical invariant of a finite gtoup, central annihilators, tight groups, condition $ ( \ast )$, fixed-point-free representations
Article copyright: © Copyright 1975 American Mathematical Society