Periodic groups saturated with finite simple symplectic groups of dimension 6 over fields of odd characteristics

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.