One Variable Equations in Torsion-free Hyperbolic Groups
نویسنده
چکیده
Let Γ be a torsion-free hyperbolic group. We show that the set of solutions of any system of equations with one variable in Γ is a finite union of points and cosets of centralizers if and only if any two-generator subgroup of Γ is free.
منابع مشابه
Conjugacy Classes of Solutions to Equations and Inequations over Hyperbolic Groups
We study conjugacy classes of solutions to systems of equations and inequations over torsion-free hyperbolic groups, and describe an algorithm to recognize whether or not there are finitely many conjugacy classes of solutions to such a system. The class of immutable subgroups of hyperbolic groups is introduced, which is fundamental to the study of equations in this context. We apply our results...
متن کاملLimit groups for relatively hyperbolic groups II: Makanin–Razborov diagrams
Let Γ be a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. We construct Makanin–Razborov diagrams for Γ. We also prove that every system of equations over Γ is equivalent to a finite subsystem, and a number of structural results about Γ–limit groups. AMS Classification numbers Primary: 20F65 Secondary: 20F67, 20E08, 57M07
متن کاملFinding relative hyperbolic structures
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” (to appear in Israel J. Math.). We study there the existential theory of torsion free hyperbolic and relatively hyperbolic group...
متن کاملSLP compression for solutions of equations with constraints in free and hyperbolic groups
The paper is a part of an ongoing program which aims to show that the existential theory in free groups (hyperbolic groups or even toral relatively hyperbolic) is NP-complete. For that we study compression of solutions with straight-line programs (SLPs) as suggested originally by Plandowski and Rytter in the context of a single word equation. We review some basic results on SLPs and give full p...
متن کاملOn equations in relatively hyperbolic groups
We investigate the problem of deciding the Diophantine theory (resp. the existential first order theory), of some torsion free relatively hyperbolic group (i.e. the problems of satisfiability of finite systems of equations (resp. of equations and inequations) with coefficients). We give a positive answer to the second problem when the parabolic subgroups are abelian, and to the first problem, m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009