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Periodic groups saturated with L 3(2m)

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Abstract

Let \(\mathfrak{M}\) be a set of finite groups. A group G is saturated with groups from \(\mathfrak{M}\) if every finite subgroup of G is contained in a subgroup isomorphic to some member of \(\mathfrak{M}\). It is proved that a periodic group G saturated with groups from the set {L3(2m)|m = 1, 2, …} is isomorphic to L3(Q), for a locally finite field Q of characteristic 2; in particular, it is locally finite.

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Authors and Affiliations

  1. Siberian Fund for Algebra and Logic, pr. Koptyug, 4, Novosibirsk, 630090, Russia

    D. V. Lytkina

  2. Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 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.

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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 606–626, September–October, 2007.

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Lytkina, D.V., Mazurov, V.D. Periodic groups saturated with L 3(2m). Algebra Logic 46, 330–340 (2007). https://doi.org/10.1007/s10469-007-0033-z

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  • DOI: https://doi.org/10.1007/s10469-007-0033-z

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