On a conjecture of Degos

Nick Gill

On a conjecture of Degos

Group Theory 2015-10-21 v2

Authors: Nick Gill

Abstract

In this note we use a result of Kantor to prove a conjecture of Degos. Specifically we prove the following: let $\mathbb{F}$ be a finite field of order $q$ and let $f, g\in\mathbb{F}[X]$ be distinct polynomials of degree $n$ such that $f$ is primitive, and the constant term of $g$ is non-zero. Then $<C_f, C_g>=\mathrm{GL}_n(q)$ .

Keywords

finite fields polynomial theory fields

Cite

@article{arxiv.1502.03341,
  title  = {On a conjecture of Degos},
  author = {Nick Gill},
  journal= {arXiv preprint arXiv:1502.03341},
  year   = {2015}
}

Comments

6 pages. This version includes a sketch-proof of a result of Kantor. The article will appear in Cah. Topol. G\'eom. Diff\'er. Cat\'eg

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