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Quotient groups of locally graded groups and groups of certain Kurosh-Chernikov classes

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Abstract

We establish the validity of the inclusion G/N∈ X for groups G ∈ X under certain restrictions on N ⊴ G, where X is one of the following classes, the class of locally graded groups, the class of RI-groups, or the class \(\hat P\mathfrak{Y}\) for a fixed group variety \(\mathfrak{Y} \supseteq \mathfrak{A}\).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    N. S. Chernikov

  2. National Pedagogic University, Kiev

    D. Ya. Trebenko

Authors
  1. N. S. Chernikov
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  2. D. Ya. Trebenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1545–1553, November, 1998.

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Chernikov, N.S., Trebenko, D.Y. Quotient groups of locally graded groups and groups of certain Kurosh-Chernikov classes. Ukr Math J 50, 1765–1773 (1998). https://doi.org/10.1007/BF02524483

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  • DOI: https://doi.org/10.1007/BF02524483

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