Journal article
A characterisation of large finitely presented groups
- Abstract:
- A group is known as `large' if some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. In this paper, we give a necessary and sufficient condition for a finitely presented group to be large, in terms of the existence of a normal series where successive quotients are finite abelian groups with sufficiently large rank and order. The proof of this result involves an analysis of the geometry and topology of finite Cayley graphs. Theorems of Baumslag and Pride, and their extensions by Gromov and Stohr, on groups with more generators than relations, follow immediately.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Version of record, pdf, 188.1KB, Terms of use)
-
- Publisher copy:
- 10.1016/j.jalgebra.2005.03.004
Authors
- Publisher:
- Elsevier
- Journal:
- Journal of Algebra More from this journal
- Volume:
- 287
- Issue:
- 2
- Pages:
- 458-473
- Publication date:
- 2005-05-15
- DOI:
- ISSN:
-
0021-8693
- Language:
-
English
- Keywords:
- Pubs id:
-
pubs:13069
- UUID:
-
uuid:fe7ce7bd-7d4d-4db9-9d9a-3b6f886dbc8c
- Local pid:
-
pubs:13069
- Source identifiers:
-
13069
- Deposit date:
-
2012-12-19
Terms of use
- Copyright holder:
- Elsevier BV
- Copyright date:
- 2005
- Notes:
- 18 pages, 6 figures; to appear in J. Algebra Copyright 2005 Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0/
- Licence:
- Other
If you are the owner of this record, you can report an update to it here: Report update to this record