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On the nilpotency index of the radical of a group algebra. VIII


Author: Kaoru Motose
Journal: Proc. Amer. Math. Soc. 92 (1984), 327-328
MSC: Primary 20C05; Secondary 16A26
DOI: https://doi.org/10.1090/S0002-9939-1984-0759645-2
MathSciNet review: 759645
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Abstract: A characterization of a finite $ p$-solvable group $ G$ with $ t(G) < (r + 2)(p - 1) + 1$ is given under certain conditions, where $ t(G)$ is the nilpotency index of the radical of a group algebra of a finite $ p$-solvable group $ G$ with a $ p$-Sylow subgroup of order $ {p^r}$ over a field of characteristic $ p$.


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

  • [1] D. Gorenstein, Finite groups, Harper & Row, New York, 1968. MR 0231903 (38:229)
  • [2] B. Huppert, Endliche Gruppen. I, Springer-Verlag, Berlin and New York, 1967. MR 0224703 (37:302)
  • [3] K. Morita, On group rings over a modular field which possess radicals expressible as principal ideals, Sci. Rep. Tokyo Bunrika Daigaku A4 (1951), 177-194. MR 0049909 (14:246a)
  • [4] K. Motose and Y. Ninomiya, On the nilpotency index of the radical of a group algebra, Hokkaido Math. J. 4 (1975), 261-264. MR 0372007 (51:8224)
  • [5] K. Motose, On a theorem of S. Koshitani, Math. J Okayama Univ. 20 (1978), 59-65. MR 0491796 (58:10995)
  • [6] -, On the nilpotency index of the radical of a group algebra. II, Math. J. Okayama Univ. 22 (1980), 141-143. MR 595794 (82c:20011)
  • [7] -, On the nilpotency index of the radical of a group algebra. III, J. London Math. Soc. 25 (1982), 39-42. MR 645863 (83d:20003)
  • [8] -, On the nilpotency index of the radical of a group algebra. V, J. Algebra (to appear). MR 757095 (86c:20009)
  • [9] -, On a theorem of Y. Tsushima, Math. J. Okayama Univ. (to appear). MR 0472895 (57:12581)
  • [10] Y. Tsushima, Some notes on the radical of a finite group ring. II, Osaka J. Math. 16 (1979), 35-38. MR 527013 (81b:20010)
  • [11] O. E. Villamayor, On the semi-simplicity of group algebras. II, Proc. Amer. Math. Soc. 10 (1959), 27-31.
  • [12] D. A. R. Wallace, Lower bounds for the radical of the group algebra of a finite $ p$-soluble group, Proc. Edinburgh Math. Soc. 16 (1968/69), 127-134. MR 0245700 (39:7006)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0759645-2
Keywords: Nilpotency index, radical, group algebra
Article copyright: © Copyright 1984 American Mathematical Society

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