New York Journal of Mathematics
Volume 15 (2009) 211-217


Herbert Abels and Roger C. Alperin

A splitting theorem for linear polycyclic groups

Published: May 28, 2009
Keywords: Polycyclic group, arithmetic group, linear group
Subject: 20H20, 20G20

We prove that an arbitrary polycyclic by finite subgroup of GL(n,\overline{Q}) is up to conjugation virtually contained in a direct product of a triangular arithmetic group and a finitely generated diagonal group.


The authors gratefully acknowledge the hospitality received at the Mathematics Department of the University of Chicago during the inception of this work.

Author information

Herbert Abels:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, GERMANY

Roger C. Alperin:
Department of Mathematics, San Jose State University, San Jose, CA 95192, USA