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Finite Groups Close to Frobenius Groups

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Abstract

We study finite nonsoluble generalized Frobenius groups; i.e., the groups G with a proper nontrivial normal subgroup F such that each coset Fx of prime order p, as an element of the quotient group G/F, consists only of p-elements. The particular example of such a group is a Frobenius group, given that F is the Frobenius kernel of G, and also the Camina group.

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References

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Authors and Affiliations

  1. Department of Mathematics and Physics, Anhui Jianzhu University, Hefei, P.R. China

    X. Wei

  2. Kabardino-Balkarian State University, Nalchik, Russia

    A. Kh. Zhurtov

  3. Siberian State University of Telecommunications and Information Sciences Novosibirsk State University, Novosibirsk, Russia

    D. V. Lytkina

  4. Sobolev Institute of Mathematics Novosibirsk State University, Novosibirsk, Russia

    V. D. Mazurov

Authors
  1. X. Wei
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  2. A. Kh. Zhurtov
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  3. D. V. Lytkina
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  4. V. D. Mazurov
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Corresponding authors

Correspondence to X. Wei, A. Kh. Zhurtov, D. V. Lytkina or V. D. Mazurov.

Additional information

Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 5, pp. 1035–1040.

The first author was supported by the NNSF of China (Grant 11771409). This research was supported by the Russian Foundation for Basic Research (Grant 19-01-00507).

The authors express gratitude to A. S. Kondratiev who drew their attention to Camina pairs, and also to the referee whose comments and suggestions allowed us to improve the manuscript significantly.

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Wei, X., Zhurtov, A.K., Lytkina, D.V. et al. Finite Groups Close to Frobenius Groups. Sib Math J 60, 805–809 (2019). https://doi.org/10.1134/S0037446619050045

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  • DOI: https://doi.org/10.1134/S0037446619050045

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