- 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.
- Publication status:
- Published
- Publisher copy:
- 10.1016/S0022-4049(02)00307-9
-
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- Journal:
- JOURNAL OF PURE AND APPLIED ALGEBRA
- Volume:
- 181
- Issue:
- 1
- Pages:
- 15-22
- Publication date:
- 2003-06-01
- DOI:
- ISSN:
-
0022-4049
- URN:
-
uuid:18ae901e-ba3c-462f-bb2a-4539bafe346c
- Source identifiers:
-
3548
- Local pid:
- pubs:3548
- Language:
- English
- Copyright date:
- 2003
Journal article
Finite presentation of fibre products of metabelian groups
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