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Finite presentation of fibre products of metabelian groups |
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| Authors: | Gilbert Baumslag Derek F Holt |
| Institution: | a Department of Mathematics, City College of New York, Convent Avenue at 138th Street, New York, NY 10031, USA b Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, UK c Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK d Department of Mathematics and Statistics, University of Melbourne, Parkville 3052, Australia |
| 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  finitely generated. |
| Keywords: | 20F05 20J05 20F16 20E22 |
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