Literature cited
G. Higman, “The units of group rings,” Proc. London Math. Soc.,36, 231–248 (1940).
S. D. Berman, “On the equation xm=1 in an integral group ring,” Ukr. Mat. Zh.,7, No. 3, 253–261 (1955).
J. A. Cohn and D. Livingstone, “On the structure of group algebras. I,” Can. J. Math.,17, No. 4, 583–593 (1965).
A. A. Bovdi, “Periodic normal subgroups of the multiplicative group of a group ring. I,” Sib. Mat. Zh.,9, No. 3, 495–498 (1968).
A. A. Bovdi, “Periodic normal subgroups of the multiplicative group of a group ring. II,” Sib. Mat. Zh.,11, No. 3, 492–511 (1970).
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.
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.
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.
L. F. Barannik, “On the Schur index of protective representations of finite groups,” Mat. Sb.,86, No. 1, 110–120 (1971).
P. Roquette, “Realisierung von Darstellungen endlicher nilpotenter Gruppen,” Arch. Math.,9, 241–250 (1958).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 35, No. 2, pp. 137–143, March–April, 1983.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01088920