Galois embedding problems with cyclic quotient of order p

Details Galois embedding problems with cyclic quotient of order p Galois embedding problems with cyclic quotient of order p

2003-09-05

arxiv.org/abs/math/0309090v2

Israel J. Math. 145 (2005), 93--112

Mathematics

Number Theory

v2 (22 pages): results extended to arbitrary fields; in particular, we establish a new automatic realization in Galois theory

Scientific paper

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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