Periodic groups saturated with finite simple groups \(L_4(q)\). (English. Russian original) Zbl 1515.20184

Guo, W.; Lytkina, D. V.; Mazurov, V. D.

Algebra Logic 60, No. 6, 360-365 (2022); translation from Algebra Logika 60, No. 6, 549-556 (2021).

Summary: 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 \(L_4(q)\), where \(q\) is odd, is isomorphic to \(L_4(F)\) for a suitable field \(F\) of odd characteristic.

MSC:

20F50

Periodic groups; locally finite groups

Keywords:

periodic group; locally finite group; involution; saturation

Software:

GAP

References:

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