On the imbedding problem for local fields

The imbedding problem of local fields is considered for the case where the whole of the group is a $p$-group having as many generators as the Galois group of the extension and the extension consists of a primitive root of 1 of degree equal to the period of the kernel. It is proved that it is necessary and sufficient for the solvability of this problem that a concordance condition (and even a weaker condition) be satisfied (see [4]).