2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68481Let 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 theoryNumber Theory12F10text