On The Periodic Groups Saturated with Finite Simple Groups of Lie Type B 3

Let $$\mathfrak{M}$$ be a set of finite groups. Given a group G, denote by $$\mathfrak{M}(G)$$ the set of all subgroups of G isomorphic to the elements of $$\mathfrak{M}$$. A group G is said to be saturated with groups from $$\mathfrak{M}$$ (saturated with $$\mathfrak{M}$$, for brevity) if each finite subgroup of G lies in an element of $$\mathfrak{M}(G)$$. We prove that a periodic group G saturated with $$\mathfrak{M}=\left\{O_{7}(q)\mid{q}\equiv\pm3(\text{mod}\;8)\right\}$$ is isomorphic to O7(F) for some locally finite field F of odd characteristic.