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Periodic Groups Saturated with Finite Simple Groups L4(q)

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Algebra and Logic Aims and scope

If M is a set of finite groups, then a group G is said to be saturated with the set M (saturated with groups in M) if every finite subgroup of G is contained in a subgroup isomorphic to some element of M. It is proved that a periodic group with locally finite centralizers of involutions, which is saturated with a set consisting of groups L4(q), where q is odd, is isomorphic to L4(F) for a suitable field F of odd characteristic.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, China

    W. Guo

  2. Hefei School of Science, Hainan University, Haikou, Hainan, P.R. China

    W. Guo

  3. Sobolev Institute of Mathematics, Novosibirsk, Russia

    D. V. Lytkina & V. D. Mazurov

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

    D. V. Lytkina

Authors
  1. W. Guo
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  2. D. V. Lytkina
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  3. V. D. Mazurov
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Correspondence to W. Guo.

Additional information

Translated from Algebra i Logika, Vol. 60, No. 6, pp. 549-556, November-December, 2021. Russian DOI: https://doi.org/10.33048/alglog.2021.60.602

Supported by the NNSF of China (grant No. 11771409) and by Key Laboratory of mathematics Wu Wen-Tsun of the Academy of Science of China.

Supported byMathematical Center in Akademgorodok, Agreement with RFMinistry of Education and Science No. 075-15-2019-1613.

Supported by RFBR (project No. 20-51-00007) and by SB RAS Fundamental Research Program I.1.1 (project No. 0314-2019-0001).

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Guo, W., Lytkina, D.V. & Mazurov, V.D. Periodic Groups Saturated with Finite Simple Groups L4(q). Algebra Logic 60, 360–365 (2022). https://doi.org/10.1007/s10469-022-09662-2

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  • DOI: https://doi.org/10.1007/s10469-022-09662-2

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