arXiv 1003.40952010-03-22math.GRmath.LO

Homogeneity in the free group

Chloé Perin, Rizos Sklinos

备注：: 26 pages
发表信息：: Duke Math. J. 161, no. 13 (2012), 2635-2668
DOI：: 10.1215/00127094-1813068

英文摘要：

We show that any non abelian free group $\F$ is strongly $\aleph_0$-homogeneous, i.e. 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 $\aleph_0$-homogeneous.

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