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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A group theoretic criterion for property FA


Authors: Marc Culler and Karen Vogtmann
Journal: Proc. Amer. Math. Soc. 124 (1996), 677-683
MSC (1991): Primary 20E08; Secondary 20F28, 20F36, 05C05
MathSciNet review: 1307506
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Abstract: We give group-theoretic conditions on a set of generators of a group $G$ which imply that $G$ admits no non-trivial action on a tree. The criterion applies to several interesting classes of groups, including automorphism groups of most free groups and mapping class groups of most surfaces.


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Additional Information

Marc Culler
Affiliation: Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607-7045
Email: culler@math.uic.edu

Karen Vogtmann
Affiliation: Department of Mathematics, Cornell University, White Hall, Ithaca, New York 14853-7901
Email: vogtmann@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03217-0
PII: S 0002-9939(96)03217-0
Keywords: Property FA, group actions on trees
Received by editor(s): May 31, 1994
Additional Notes: Both authors are partially supported by the National Science Foundation.
Communicated by: James West
Article copyright: © Copyright 1996 American Mathematical Society