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Groups with given properties of finite subgroups

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Algebra and Logic Aims and scope

Suppose that in every finite even order subgroup F of a periodic group G, the equality [u, x]2 = 1 holds for any involution u of F and for an arbitrary element x of F. Then the subgroup I generated by all involutions in G is locally finite and is a 2-group. In addition, the normal closure of every subgroup of order 2 in G is commutative.

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Authors and Affiliations

  1. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    D. V. Lytkina & V. D. Mazurov

  2. Siberian State University of Telecommunications and Information Sciences, ul. Kirova 86, Novosibirsk, 630102, Russia

    D. V. Lytkina

  3. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    V. D. Mazurov

Authors
  1. D. V. Lytkina
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  2. V. D. Mazurov
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Correspondence to D. V. Lytkina.

Additional information

Supported by RFBR (grants No. 11-01-00456 and 11-01-91158) and by the Federal Program “Scientific and Scientific-Pedagogical Cadres of Innovative Russia” for 2009-2013 (gov. contract No. 14.740.11.0346).

Translated from Algebra i Logika, Vol. 51, No. 3, pp. 321-330, May-June, 2012.

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Lytkina, D.V., Mazurov, V.D. Groups with given properties of finite subgroups. Algebra Logic 51, 213–219 (2012). https://doi.org/10.1007/s10469-012-9184-7

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  • DOI: https://doi.org/10.1007/s10469-012-9184-7

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