Abstract
The embedding problem, which is the problem of extending a given Galois extension K 3 k to a Galois extension L 3 K 3 k so that G(L/k) is a prescribed group extension of G(K/k), is investigated in the case k is a number field and G(L/K) is nonsolvable, with respect o the question of reduction methods. Two general (arbitrary k and G(L/K)) reduction theorems are proved, one reducing the general problem to the cases of G(L/K) nilpotent, and split group extensions, resp., and the second reducing the problem in the case G(L/K) having trivial center to the case G(L/k) F aut G(L/K). The notion of localixability of an embedding problem is formulated and investigated for certain classical groups.
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