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Group algebras of periodic groups of a solvable multiplicative group

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Abstract

The structure of the group algebra KG of an arbitrary periodic group G such that the multiplicative group U(KG) is solvable is completely determined.

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Literature cited

  1. J. M. Bateman, “On the solvability of unit groups of group algebras,” Trans. Am. Math. Soc.,157, 73–86 (1971).

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  2. K. Motose and Y. Ninomiya, “On the solvability of unit groups of group rings,” Math. J. Okayama Univ.,15, 209–214 (1972).

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  3. A. A. Bovdi and I. I. Khripta, “Finite-dimensional group algebras with solvable multiplicative group,” in: Proceedings of the Eighteenth Scientific Conference at State University, Mathematical Science-Section [in Russian], Uzhgorod (1974).

  4. I. B. Passi, D. Passman, and S. K. Sehgal, “Lie solvable group rings,” Canad. J. Math.,25, 748–757 (1973).

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  5. A. A. Bovdi, Group Rings [in Russian], Izd. Uzhgorodskii Cos. Univ. (1974).

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Authors and Affiliations

  1. Drogobychskii Pedagogic Institute, USSR

    A. A. Bovdi & I. I. Khripta

Authors
  1. A. A. Bovdi
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  2. I. I. Khripta
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Translated from Matematicheskie Zametki, Vol. 22, No. 3, pp. 421–432, September, 1977.

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Bovdi, A.A., Khripta, I.I. Group algebras of periodic groups of a solvable multiplicative group. Mathematical Notes of the Academy of Sciences of the USSR 22, 725–731 (1977). https://doi.org/10.1007/BF02412503

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  • DOI: https://doi.org/10.1007/BF02412503

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