Universally concordant Galois extensions

A Galois extension is called universally concordant of period q, if for any imbedding problem of this extension whose kernel is an Abelian group of period q the concordance condition is satisifed. A necessary and sufficient condition is given for the imbeddability of one universally concordant extension into another. For a universally concordant extension of period of an algebraic number field containing no roots of 1 of degrees p₁, ..., p_m the solvability of any imbedding problem with solvable kernel of period q is proved.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 71, pp. 133–152, 1977.