Elementary theory of free non-abelian groups

By Olga Kharlampovich, Alexei G. Myasnikov. 2006

254 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7d04edc6969c5846cbb2436e5756105a00b4316f

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In Computational Theory and Mathematics

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Citations in the corpus

Limit groups for relatively hyperbolic groups. I. The basic tools (2004, background): “In particular, Sela answers in the positive some longstanding questions of Tarski (Kharlampovich and Miasnikov have another approach to these problems; see [30]).”
Effective JSJ Decompositions (2004, methodology): “A variation of Theorem 1 first appeared in [39] (in terms of the elimination processes), where it was used in the proof of the second Tarski’s conjecture on the decidability of the elementary theory of free non-abelian groups.”
Unification theorems in algebraic geometry (2008, background): “…over G [4, 24, 25, 26, 47], groups universally equivalent to G [40, 13, 34], limit groups of G in the Grigorchuk-Gromov’s metric [10], in the theory of equations in groups [28, 38, 39, 24, 25, 26, 18], in group actions [8, 12, 35, 17, 14], in the solutions of Tarski problems [27, 48], etc.”
Foliations for solving equations in groups: free, virtually free, and hyperbolic groups (2009, background): “It has also been, together with these developments, a prelude to the far-reaching recent solutions to Tarski’s problems on the elementary theory of free groups, by Sela [47], and by Kharlampovich and Miasnikov [27].”
Subgroups of direct products of limit groups (2007, background): “…should consult the introductions in [1, 6], the original papers of Sela [22, 23, 24], or those of Kharlampovich and Myasnikov [18, 19, 20] where the subject is approached from a perspective more in keeping with traditional combinatorial group theory; a further perspective is developed in [16].”
Homogeneity and prime models in torsion-free hyperbolic groups (2010, background): “Sela [38] and Kharlampovich and Myasnikov [11] show that nonabelian free groups have the same elementary theory and, in fact, the following more explicit description.”
Normal automorphisms of relatively hyperbolic groups (2008, background): “The class of relatively hyperbolic groups includes (ordinary) hyperbolic groups, fundamental groups of finite-volume complete Riemannian manifolds of pinched negative curvature [7, 14], groups acting freely on R-trees [20] (in particular, limit groups arising in the solutions of the Tarski problem [”