Abstract: | A survey of solvability conditions for the embedding problem of number fields, in which the kernel is a non-Abelian group of order p4, is completed. As a kernel, the two 2-groups with two generators a, b and with the following relations are considered: a 8 =1, b 2 =1, [a,b]=a−2 in the first group, and a 8 =1, b 2 =a 4 , [a,b]=a−2 in the second. Bibliography: 7 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 127–132. Translated by V. V. Ishkhanov. |