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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stable representatives for symmetric automorphisms of groups and the general form of the Scott conjecture


Author: Mihalis Sykiotis
Journal: Trans. Amer. Math. Soc. 356 (2004), 2405-2441
MSC (2000): Primary 20E36, 20E08, 20E06
Published electronically: November 12, 2003
MathSciNet review: 2048523
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Abstract: Let $G$ be a group acting on a tree $X$ such that all edge stabilizers are finite. We extend Bestvina-Handel's theory of train tracks for automorphisms of free groups to automorphisms of $G$ which permute vertex stabilizers. Using this extension we show that there is an upper bound depending only on $G$ for the complexity of the graph of groups decomposition of the fixed subgroups of such automorphisms of $G$.


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Additional Information

Mihalis Sykiotis
Affiliation: Department of Mathematics, University of Athens, Athens 15784, Greece
Address at time of publication: Amalthias 18, Larisa 41222, Greece
Email: msikiot@cc.uoa.gr

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03385-3
PII: S 0002-9947(03)03385-3
Received by editor(s): July 24, 2002
Received by editor(s) in revised form: April 17, 2003
Published electronically: November 12, 2003
Article copyright: © Copyright 2003 American Mathematical Society