Duke Mathematical Journal

Homogeneity in the free group

Chloé Perin and Rizos Sklinos

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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.

Article information

Source
Duke Math. J., Volume 161, Number 13 (2012), 2635-2668.

Dates
First available in Project Euclid: 11 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1349960279

Digital Object Identifier
doi:10.1215/00127094-1813068

Mathematical Reviews number (MathSciNet)
MR2988905

Zentralblatt MATH identifier
1270.20028

Subjects
Primary: 20E05: Free nonabelian groups
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups 03C07: Basic properties of first-order languages and structures

Citation

Perin, Chloé; Sklinos, Rizos. Homogeneity in the free group. Duke Math. J. 161 (2012), no. 13, 2635--2668. doi:10.1215/00127094-1813068. https://projecteuclid.org/euclid.dmj/1349960279


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