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- Title
Conjugacy separability of 1-acylindrical graphs of free groups.
- Authors
Cotton-Barratt, Owen; Wilton, Henry
- Abstract
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.
- Subjects
GROUP theory; ABSTRACT algebra; ALGEBRAIC field theory; TREE graphs; PROFINITE groups; FREE groups; CONJUGACY classes
- Publication
Mathematische Zeitschrift, 2012, Vol 272, Issue 3/4, p1103
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-012-0978-z