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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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