On characterization of simple orthogonal groups of odd dimension in the class of periodic groups. (English. Russian original) Zbl 1498.20093

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

Sib. Math. J. 62, No. 1, 77-83 (2021); translation from Sib. Mat. Zh. 62, No. 1, 97-105 (2021).

Summary: Suppose that \(n\) is an integer, \( n\geq 3 \). We prove that a periodic group saturated with a set of the finite simple groups \(O_{2n+1}(q) \), where \(q\) is congruent to \(\pm 3\) modulo 8, is isomorphic to \(O_{2n+1}(F)\) for some locally finite field \(F \).

MSC:

20F50

Periodic groups; locally finite groups

Keywords:

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

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