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ALGEBRAIC AND DEFINABLE CLOSURE IN FREE GROUPS

机译：ALGEBRAIC AND DEFINABLE CLOSURE IN FREE GROUPS

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摘要

We study algebraic closure and its relation with definable closure in free groups and more generally in torsion-free hyperbolic groups. Given a torsion-free hyperbolic group Gamma and a nonabelian subgroup A of Gamma, we describe Gamma as a constructible group from the algebraic closure of A along cyclic subgroups. In particular, it follows that the algebraic closure of A is finitely generated, quasiconvex and hyperbolic.

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