Galois embedding problems with cyclic quotient of order p
Abstract
Description
Let K/F be a cyclic field extension of odd prime degree. We consider Galois embedding problems involving Galois groups with common quotient Gal(K/F) such that corresponding normal subgroups are indecomposable Fp[Gal(K/F)]-modules. For these embedding problems we prove conditions on solvability, formulas for explicit construction, and results on automatic realizability.
v2 (22 pages): results extended to arbitrary fields; in particular, we establish a new automatic realization in Galois theory
v2 (22 pages): results extended to arbitrary fields; in particular, we establish a new automatic realization in Galois theory