Periodic groups saturated with finite simple symplectic groups of dimension \(6\) over fields of odd characteristics. (English. Russian original) Zbl 07637846

Lytkina, D. V.; Mazurov, V. D.

Sib. Math. J. 63, No. 6, 1117-1120 (2022); translation from Sib. Mat. Zh. 63, No. 6, 1308-1312 (2022).

Summary: We prove that a periodic group is locally finite, if its every finite subgroup lies in a subgroup isomorphic to a simple symplectic group of dimension 6 over some field of odd order and the centralizer of every involution of this group is locally finite. Moreover, such group is isomorphic to a simple symplectic group of dimension 6 over a suitable locally finite field of odd characteristic.

MSC:

20G40	Linear algebraic groups over finite fields
20E32	Simple groups
20F50	Periodic groups; locally finite groups

Keywords:

periodic group; locally finite group; group of Lie type; group saturated with set of groups

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