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Crossed group rings in which solutions of the equation xn − μ = 0 are trivial

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Literature cited

  1. G. Higman, “The units of group rings,” Proc. London Math. Soc.,36, 231–248 (1940).

    Google Scholar 

  2. S. D. Berman, “On the equation xm=1 in an integral group ring,” Ukr. Mat. Zh.,7, No. 3, 253–261 (1955).

    Google Scholar 

  3. J. A. Cohn and D. Livingstone, “On the structure of group algebras. I,” Can. J. Math.,17, No. 4, 583–593 (1965).

    Google Scholar 

  4. A. A. Bovdi, “Periodic normal subgroups of the multiplicative group of a group ring. I,” Sib. Mat. Zh.,9, No. 3, 495–498 (1968).

    Google Scholar 

  5. A. A. Bovdi, “Periodic normal subgroups of the multiplicative group of a group ring. II,” Sib. Mat. Zh.,11, No. 3, 492–511 (1970).

    Google Scholar 

  6. M. S. Semirot, “Crossed group rings with the identity xx*=x*x,” in: Materials of the First Conference of Young Scientists of the Zakhid Scientific Center of the Academy of Sciences of the Ukrainian SSR, Mathematics and Mechanics Section, No. 313-74 Dep., VINITI, 1974 (Uzhgorod, 1973), pp. 28–37.

  7. A. F. Barannik and L. F. Barannik, “Crossed group rings with trivial multiplicative group,” in: Materials of the Thirty-First Concluding Scientific Conference of Professorial and Teaching Personnel of Uzhgorod University, Mathematical Sciences Section, No. 3131-78 Dep., VINITI, 1978 (Uzhgorod, 1978), pp. 119–136.

  8. L. F. Barannik and A. F. Barannik, “On the equation xn=μ in an integral crossed group ring,” in: Materials of the Thirty-First Concluding Scientific Conference of Professorial and Teaching Personnel of Uzhgorod University, Mathematical Sciences Section, No. 3131-78 Dep., VINITI, 1978 (Uzhgorod, 1978), pp. 98–118.

  9. L. F. Barannik, “On the Schur index of protective representations of finite groups,” Mat. Sb.,86, No. 1, 110–120 (1971).

    Google Scholar 

  10. P. Roquette, “Realisierung von Darstellungen endlicher nilpotenter Gruppen,” Arch. Math.,9, 241–250 (1958).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 35, No. 2, pp. 137–143, March–April, 1983.

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Barannik, A.F., Barannik, L.F. Crossed group rings in which solutions of the equation xn − μ = 0 are trivial. Ukr Math J 35, 119–124 (1983). https://doi.org/10.1007/BF01088920

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