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On Property (FA) for wreath products

Abstract:
We characterize permutational wreath products with Property (FA). For instance, the standard wreath product A wr B of two nontrivial countable groups A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely generated group with finite abelianisation. We also prove an analogous result for hereditary Property (FA). On the other hand, we prove that many wreath products with hereditary Property (FA) are not quotients of finitely presented groups with the same property.
Publication status:
Published

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Publisher copy:
10.1515/jgt.2010.044

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
J. Group Theory 14(1) (2011) 165-174
Volume:
14
Issue:
1
Pages:
165-174
Publication date:
2010-04-15
DOI:
EISSN:
1435-4446
ISSN:
1433-5883
URN:
uuid:269d716b-7451-4a44-8c06-b291456c51fc
Source identifiers:
187867
Local pid:
pubs:187867

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