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Galois embedding problems with cyclic quotient of order p

Jan Minac·John Swallow
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Abstract

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.

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Jan Minac, John Swallow. 2004-04-08. Galois embedding problems with cyclic quotient of order p. https://arxiv.org/abs/math/0309090

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