Jan Minac & John Swallow: Galois embedding problems with cyclic quotient of order p

minac@uwo.ca, joswallow@davidson.edu

Submission: 2003, Aug 21

Let $K$ be a cyclic Galois extension of degree $p$ over a field $F$ containing a primitive $p$th root of unity. 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.

2000 Mathematics Subject Classification:

Keywords and Phrases:

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