Let be a matrix in GL of infinite order. In a recent paper, G. Levitt and V. Metaftsis prove that for any sufficiently large integer the matrix is not conjugated to a companion matrix. We first prove a local version of this theorem. Then, we give an effective statement, using diophantine methods. We also discuss several related problems.
Cite this article
Francesco Amoroso, Umberto Zannier, Some remarks concerning the rank of mapping tori and ascending HNN-extensions of abelian groups. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 23 (2012), no. 2, pp. 197–211DOI 10.4171/RLM/624