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On representations of m-groups

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Abstract

We obtain a description of the m-transitive representations of an arbitrary m-group. Some necessary and sufficient conditions are given for an m-group to admit a faithful m-transitive representation. We establish as a corollary that each subdirectly m-indecomposable group admits a faithful m-transitive representation, and so each variety of m-groups is generated by its m-transitive groups.

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Authors and Affiliations

  1. Altai State University, Barnaul, Russia

    S. V. Varaksin

  2. Altai State University of Agriculture, Barnaul, Russia

    A. V. Zenkov

Authors
  1. S. V. Varaksin
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  2. A. V. Zenkov
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Correspondence to S. V. Varaksin.

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Original Russian Text Copyright © 2013 Varaksin S.V. and Zenkov A.V.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 2, pp. 298–302, March–April, 2013.

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Varaksin, S.V., Zenkov, A.V. On representations of m-groups. Sib Math J 54, 227–230 (2013). https://doi.org/10.1134/S0037446613020067

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  • DOI: https://doi.org/10.1134/S0037446613020067

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