Journal article
Free product decompositions in images of certain free products of groups
- Abstract:
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Let F be the free product of n groups and let R be a normal subgroup generated (as a normal subgroup) by m elements of F, where m < n. The Main Theorem gives sufficient conditions for families of fewer than n−m subgroups in certain quotients of F/R to generate their free product. This leads to a more direct proof of a result of the first author, that if G is a group having a presentation with n generators and m relators, where m < n, then any generating set for G contains n−m elements that freely generate a free subgroup of G. Another consequence is that an n-generator one-relator group cannot be generated by fewer than n−1 subgroups each having a non-trivial abelian normal subgroup.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 158.7KB, Terms of use)
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- Publisher copy:
- 10.1016/j.jalgebra.2006.08.008
Authors
- Publisher:
- Elsevier
- Journal:
- JOURNAL OF ALGEBRA More from this journal
- Volume:
- 310
- Issue:
- 1
- Pages:
- 57-69
- Publication date:
- 2007-04-01
- DOI:
- ISSN:
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0021-8693
- Language:
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English
- Keywords:
- Pubs id:
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pubs:2953
- UUID:
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uuid:0ba5edae-22dc-4bb8-be27-5ef5c55d7d0e
- Local pid:
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pubs:2953
- Source identifiers:
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2953
- Deposit date:
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2012-12-19
Terms of use
- Copyright holder:
- Elsevier BV
- Copyright date:
- 2007
- Notes:
- Copyright 2006 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
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