Imbedding problem with a noncommutative kernel of order p4. II

The problem of imbedding number fields is investigated for p-groups, where the kernel is a non-Abelian group of order p⁴ with two generators , and relationsIt is shown that the solvability of this problem is equivalent to the simultaneous solvability of all the collateral local problems and the collateral Abelian problem obtained by the factorization of the kernel by the derived group.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 101–113, 1991.