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1 October 2012 Homogeneity in the free group
Chloé Perin, Rizos Sklinos
Duke Math. J. 161(13): 2635-2668 (1 October 2012). DOI: 10.1215/00127094-1813068

Abstract

We show that any nonabelian free group F is strongly 0-homogeneous, that is, that finite tuples of elements which satisfy the same first-order properties are in the same orbit under Aut(F). We give a characterization of elements in finitely generated groups which have the same first-order properties as a primitive element of the free group. We deduce as a consequence that most hyperbolic surface groups are not strongly 0-homogeneous.

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Chloé Perin. Rizos Sklinos. "Homogeneity in the free group." Duke Math. J. 161 (13) 2635 - 2668, 1 October 2012. https://doi.org/10.1215/00127094-1813068

Information

Published: 1 October 2012
First available in Project Euclid: 11 October 2012

zbMATH: 1270.20028
MathSciNet: MR2988905
Digital Object Identifier: 10.1215/00127094-1813068

Subjects:
Primary: 20E05
Secondary: 03C07, 20F67

Rights: Copyright © 2012 Duke University Press

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Vol.161 • No. 13 • 1 October 2012
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