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 pre...
