On a conjecture of Degos

zbMath1368.20065arXiv1502.03341MaRDI QIDQ3178886

Nick Gill

Publication date: 20 December 2016

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 $f, ginmathbb{F}[X]$ be distinct polynomials of degree $n$ such that $f$ is primitive, and the constant term of $g$ is non-zero. Then $<C_f, C_g>=mathrm{GL}_n(q)$.

Full work available at URL: https://arxiv.org/abs/1502.03341

zbMATH Keywords

finite fieldsgeneral linear groupcompanion matricesgroup generation

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Other matrix groups over finite fields (20H30)

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