Abstract
We obtain a generalization of the Gaschutz criterion of existence of exact irreducible representations of finite groups to the class of normal groups.
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References
D. J. S. Robinson,Finiteness Conditions and Generalized Soluble Groups, Springer Verlag, Berlin (1972).
W. Gaschutz, “Endliche Gruppen mit treuen absolutirreduziblen Darstellungen,”Math. Nachr.,12, No. 3/4, 253–255 (1954).
É. M. Zhmud', “On isomorphic linear representations of finite groups,”Mat. Sb.,38, No. 4, 417–430 (1956).
A. V. Tushev, “Irreducible representations of locally polycyclic groups over an absolute field,”Ukr. Mat. Zh.,42, No. 10, 1389–1394 (1990).
D. J. S. Robinson and Z. Zhang, “Groups whose proper quotients have finite derived subgroups,”J. Algebra,118, 346–368 (1988).
L. Fuchs,Infinite Abelian Groups. Vol. II, Academic Press, New York-London (1973).
S. Lang,Algebra [Russian translation], Mir, Moscow (1968).
N. Bourbaki,Modules, Rings, Forms [Russian translation], Nauka, Moscow (1966).
J. S. Wilsin, “Some properties of groups inherited by normal subgroups of finite index,”Math. Z.,144, No. 1. 19–21 (1970).
K. S. Brown,Cohomology of Groups, Springer-Verlag, New York-Heidelberg-Berlin (1982).
A. Guichardet,Cohomologie des Groupes Topologiques et des Algebres de Lie, Cedic/Fernand, Nathan, Paris (1980).
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Translated from Ukrainskii Matematicheskii Zhumal, Vol. 45, No. 12, pp. 1688–1694, December, 1993.
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Tushev, A.V. On exact irreducible representations of locally normal groups. Ukr Math J 45, 1900–1906 (1993). https://doi.org/10.1007/BF01061360
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DOI: https://doi.org/10.1007/BF01061360