Highly mobile Einstein spaces in the large

We consider an Einstein spaceV of the Petrov type II or III admitting a group of motionsG of high order. First we calculate the composition law and topological structure ofG. ThenV (or its submanifolds of transitivity) is represented as the homogeneous spaceG/H ofG,H being a subgroup ofG, and the actionG onV and the topology ofV are determined. The topologies of the spacesV are as follows: ⁴ (spaceT*₂), ⁴ of ³ T¹ (spaceT ₂), ⁴ (spaceT*₃), ³ (submanifolds of transitivity in spaceT ₃).In two cases (spacesT ₂ andT ₃) we have obtained metrics free of singularities.