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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

Karen Vogtmann
Affiliation: Department of Mathematics, Cornell University, White Hall, Ithaca, New York 14853-7901

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