Explicit Constructions of the non-Abelian $p^3$-Extensions Over $\QQ$

Oz Ben-Shimol

Explicit Constructions of the non-Abelian $p^3$-Extensions Over $\QQ$

Number Theory 2008-09-23 v6

Authors: Oz Ben-Shimol

Abstract

Let $p$ be an odd prime. Let $F/k$ be a cyclic extension of degree $p$ and of characteristic different from $p$ . The explicit constructions of the non-abelian $p^{3}$ -extensions over $k$ , are induced by certain elements in ${F(\mu_{p})}^{*}$ . In this paper we let $k=\QQ$ and present sufficient conditions for these elements to be suitable for the constructions. Polynomials for the non-abelian groups of order 27 over $\QQ$ are constructed.

Keywords

finite groups abelian groups finite fields

Cite

@article{arxiv.0806.2202,
  title  = {Explicit Constructions of the non-Abelian $p^3$-Extensions Over $\QQ$},
  author = {Oz Ben-Shimol},
  journal= {arXiv preprint arXiv:0806.2202},
  year   = {2008}
}

Comments

10 pages. Keywords: Constructive Galois Theory; Heisenberg group, Explicit Embedding problem. Corrections: we revised the proof of Theorem 3.1

Explicit Constructions of the non-Abelian $p^3$-Extensions Over $\QQ$

Abstract

Keywords

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