Test elements in torsion-free hyperbolic groups

Abstract

We prove that in a torsion-free hyperbolic group, an element is a test element if and only if it is not contained in a proper retract.

6 pages. v2: Minor changes as suggested by referee. Final version, to appear in New York Journal of Mathematics

References in corpus (3)

• JSJ decompositions: definitions, existence, uniqueness. I: The JSJ deformation space
• JSJ decompositions: definitions, existence, uniqueness. II. Compatibility and acylindricity
• Conjugacy classes of solutions to equations and inequations over hyperbolic groups