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Free product decompositions in images of certain free products of groups

Abstract:

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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Publisher copy:
10.1016/j.jalgebra.2006.08.008

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author


Publisher:
Elsevier
Journal:
JOURNAL OF ALGEBRA More from this journal
Volume:
310
Issue:
1
Pages:
57-69
Publication date:
2007-04-01
DOI:
ISSN:
0021-8693


Language:
English
Keywords:
Pubs id:
pubs:2953
UUID:
uuid:0ba5edae-22dc-4bb8-be27-5ef5c55d7d0e
Local pid:
pubs:2953
Source identifiers:
2953
Deposit date:
2012-12-19

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