New York Journal of Mathematics
Volume 10 (2004) 287-294


W. A. Bogley and J. Harlander

Improving tameness for metabelian groups

Published: October 13, 2004
Keywords: metabelian group, finiteness properties, Sigma theory, tame module
Subject: Primary 20F16, Secondary 20J06

We show that any finitely generated metabelian group can be embedded in a metabelian group of type F3. More generally, we prove that if n is a positive integer and Q is a finitely generated abelian group, then any finitely generated ZQ-module can be embedded in a module that is n-tame. Combining with standard facts, the F3 embedding theorem follows from this and a recent theorem of R. Bieri and J. Harlander.

Author information

W. A. Bogley:
Department of Mathematics, Oregon State University, Corvallis, OR 97331-4605

J. Harlander:
Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101-5730