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On The Periodic Groups Saturated with Finite Simple Groups of Lie Type B3

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Abstract

Let \(\mathfrak{M}\) be a set of finite groups. Given a group G, denote by \(\mathfrak{M}(G)\) the set of all subgroups of G isomorphic to the elements of \(\mathfrak{M}\). A group G is said to be saturated with groups from \(\mathfrak{M}\) (saturated with \(\mathfrak{M}\), for brevity) if each finite subgroup of G lies in an element of \(\mathfrak{M}(G)\). We prove that a periodic group G saturated with \(\mathfrak{M}=\left\{O_{7}(q)\mid{q}\equiv\pm3(\text{mod}\;8)\right\}\) is isomorphic to O7(F) for some locally finite field F of odd characteristic.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian State University of Telecommunications and Information Sciences, Novosibirsk, Russia

    D. V. Lytkina

  2. Sobolev Institute of Mathematics, 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 or V. D. Mazurov.

Additional information

In honor of the 80th birthday of Yuri Leonidovich Ershov.

Russian Text Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 634–640.

The work of D. V. Lytkina was supported by the Mathematical Center in Akademgorodok under Agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation; the work of V. D. Mazurov was supported by the Russian Science Foundation (Project 19-11-00039).

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Lytkina, D.V., Mazurov, V.D. On The Periodic Groups Saturated with Finite Simple Groups of Lie Type B3. Sib Math J 61, 499–503 (2020). https://doi.org/10.1134/S0037446620030118

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  • DOI: https://doi.org/10.1134/S0037446620030118

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