Improving tameness for metabelian groups
نویسندگان
چکیده
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.
منابع مشابه
Improving Finiteness Properties for Metabelian Groups
We show that any finitely generated metabelian group can be embedded in a metabelian group of type F3. The proof builds upon work of G. Baumslag [4], who independently with V. R. Remeslennikov [10] proved that any finitely generated metabelian group can be embedded in a finitely presented one. We also rely essentially on the Sigma theory of R. Bieri and R. Strebel [7], who introduced this geome...
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