On Characterization of Simple Orthogonal Groups of Odd Dimension in the Class of Periodic Groups

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 $ .