The paper considers the problem of full transitivity of a cotorsion hull of a separable primary group G when a ring of endomorphisms E(G) of the group G has the form , where E_s(G) is a subring of small endomorphisms of the ring E(G), whereas J_p is a ring of integer P-adic numbers. Investigation of the issue of full transitivity of a group is essentially helpful in studying its fully invariant subgroups as well as the lattice formed by these subgroups. It is proved that in the considered case, the cotorsion hull is not fully transitive. A lemma is proposed, which can be used in the study of full transitivity of a group and in other cases.