Twisted Conjugacy Classes for Polyfree Groups
نویسندگان
چکیده
منابع مشابه
Twisted Conjugacy Classes in Nilpotent Groups
A group is said to have the R∞ property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R∞ property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n ≥ 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point ...
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 کاملCOMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS
Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...
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: 2013
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2012.707718