Conjugacy separability of 1-acylindrical graphs of free groups

Details Conjugacy separability of 1-acylindrical graphs of free groups Conjugacy separability of 1-acylindrical graphs of free groups

2009-05-30

arxiv.org/abs/0906.0101v1

Mathematics

Group Theory

14 pages

Scientific paper

We use the theory of group actions on profinite trees to prove that the fundamental group of a finite, 1-acylindrical graph of free groups with finitely generated edge groups is conjugacy separable. This has several applications: we prove that positive, $C'(1/6)$ one-relator groups are conjugacy separable; we provide a conjugacy separable version of the Rips construction; we use this latter to provide an example of two finitely presented, residually finite groups that have isomorphic profinite completions, such that one is conjugacy separable and the other does not even have solvable conjugacy problem.

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