Completely solvable imbedding problems with Abelian kernel for local fields

The imbedding problem for $p$-groups is considered in which the fields are assumed to be local and the kernel commutative. Additional conditions are investigated under which a solvable imbedding problem has a field as solution. Sufficient conditions are found for such solvability in the form of inequalities imposed on the number of generators of certain groups. Bibl. 5 titiles.