منابع مشابه
The Geometry of Twisted Conjugacy Classes in Wreath Products
We give a geometric proof based on recent work of Eskin, Fisher and Whyte that the lamplighter group Ln has infinitely many twisted conjugacy classes for any automorphism φ only when n is divisible by 2 or 3, originally proved by Gonçalves and Wong. We determine when the wreath product G o Z has this same property for several classes of finite groups G, including symmetric groups and some nilpo...
متن کاملRemnant inequalities and doubly-twisted conjugacy in free groups
We give two results for computing doubly-twisted conjugacy relations in free groups with respect to homomorphisms φ and ψ such that certain remnant words from φ are longer than the images of generators under ψ. Our first result is a remnant inequality condition which implies that two words u and v are not doubly-twisted conjugate. Further we show that if ψ is given and φ, u, and v are chosen at...
متن کاملSingleton doubly-twisted conjugacy classes in free groups
We give a simple method which can be used to show that an element of a free group is the only member of its doubly-twisted conjugacy class with respect to a pair of homomorphisms having a natural remnant property. We also show that most pairs of homomorphisms have infinitely many such singleton classes.
متن کاملComputing twisted conjugacy classes in free groups using nilpotent quotients
There currently exists no algebraic algorithm for computing twisted conjugacy classes in free groups. We propose a new technique for deciding twisted conjugacy relations using nilpotent quotients. Our technique is a generalization of the common abelianization method, but admits significantly greater rates of success. We present experimental results demonstrating the efficacy of the technique, a...
متن کاملTwisted Conjugacy in Braid Groups
In this note we solve the twisted conjugacy problem for braid groups, i.e. we propose an algorithm which, given two braids u, v ∈ Bn and an automorphism φ ∈ Aut(Bn), decides whether v = (φ(x))−1ux for some x ∈ Bn. As a corollary, we deduce that each group of the form Bn o H, a semidirect product of the braid group Bn by a torsion-free hyperbolic group H, has solvable conjugacy problem.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2020
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2020.1751848