English

Galois embedding problems with cyclic quotient of order p

Number Theory 2007-05-23 v2

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.

Keywords

Cite

@article{arxiv.math/0309090,
  title  = {Galois embedding problems with cyclic quotient of order p},
  author = {Jan Minac and John Swallow},
  journal= {arXiv preprint arXiv:math/0309090},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T16:57:26.224Z