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Finite presentation of fibre products of metabelian groups

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

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
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

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