Shunkov groups saturated with general linear groups. (English. Russian original) Zbl 1347.20038

Shlepkin, A. A.

Sib. Math. J. 57, No. 1, 174-184 (2016); translation from Sib. Mat. Zh. 57, No. 1, 222-235 (2016).

Summary: We prove that if a periodic Shunkov group is saturated with degree 2 general linear groups over finite fields then it is isomorphic to the degree 2 general linear group over a suitable locally finite field.

MSC:

20F50	Periodic groups; locally finite groups
20G15	Linear algebraic groups over arbitrary fields
20E25	Local properties of groups
20E07	Subgroup theorems; subgroup growth
20G40	Linear algebraic groups over finite fields

Keywords:

periodic Shunkov groups; groups saturated by sets of groups; periodic groups; saturating sets; finite general linear groups; finite subgroups; general linear groups over locally finite fields

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