Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structures

Details Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structures Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structures

2005-05-16

arxiv.org/abs/math/0505345v4

1st part: Israel J. Math 173 (2009) 91-124; 2nd part: Bull. London Math. Soc. 40 no.3 (2008), 395-404.

Mathematics

Group Theory

Two independant parts 23p + 9p, revised. To appear separately in Israel J. Math, and Bull. London Math. Soc. respectively

Scientific paper

This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in (relatively) hyperbolic groups". We study there the existential theory of torsion free hyperbolic and relatively hyperbolic groups, in particular those with virtually abelian parabolic subgroups. We show that the satisfiability of systems of equations and inequations is decidable in these groups. In the second part, called "Finding relative hyperbolic structures", we provide a general algorithm that recognizes the class of groups that are hyperbolic relative to abelian subgroups.

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