Journal article
Finite presentation of fibre products of metabelian groups
G Baumslag, MR Bridson, DF Holt, CF Miller
Journal of Pure and Applied Algebra | ELSEVIER SCIENCE BV | Published : 2003
Abstract
We show that if Γ is a finitely presented metabelian group, then the "untwisted" fibre product or pull-back P associated to any short exact sequence 1→N→Γ→Q→1 is again finitely presented. In contrast, if N and Q are abelian, then the analogous "twisted" fibre-product is not finitely presented unless Γ is polycyclic. Also a number of examples are constructed, including a non-finitely presented metabelian group P with H2(P,ℤ) finitely generated. © 2003 Elsevier Science B.V. All rights reserved.