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Proceedings of the American Mathematical Society

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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
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.


References [Enhancements On Off] (What's this?)

  • [1] J. S. Hsia and Roger D. Peterson, An invariant ideal of a group ring of a finite group, and applications, J. Algebra 32 (1974), no. 3, 576–599. MR 0384908
  • [2] David Ford, J. S. Hsia and R. D. Peterson, Some computations of the numerical invariant of a finite group (in preparation).
  • [3] M. Knebusch and W. Scharlau, Über das Verhalten der Witt-Gruppe bei galoischen Körpererweiterungen, Math. Ann. 193 (1971), 189–196 (German). MR 0292873
  • [4] Winfried Scharlau, Eine Invariante endlicher Gruppen, Math. Z. 130 (1973), 291–296 (German). MR 0322035
  • [5] Michio Suzuki, On finite groups with cyclic Sylow subgroups for all odd primes, Amer. J. Math. 77 (1955), 657–691. MR 0074411

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Additional Information

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