Related papers: Decision problems, complexity, traces, and represe…
We construct a class of finitely generated groups which have arbitrarily large conjugacy separability function, but in which the conjugacy problem can be solved in polynomial time, demonstrating that the McKinsey algorithm for the conjugacy…
We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that…
The conjugacy problem for a finitely generated group $G$ is the two-variable problem of deciding for an arbitrary pair $(u,v)$ of elements of $G$, whether or not $u$ is conjugate to $v$ in $G$. We construct examples of finitely generated,…
Let $G$ be a classical group defined over a finite field. We consider the following fundamental problems concerning conjugacy in $G$: 1. List a representative for each conjugacy class of $G$. 2. Given $x \in G$, describe the centralizer of…
Many results have been established that show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper is to show several results about solvability concerning the…
Separability for groups refers to the question which subsets of a group can be detected in its finite quotients. Classically, separability is studied in terms of which classes have a certain separability property, and this question is…
We study the conjugacy problem in cyclic extensions of free groups. It is shown that the conjugacy problem is solvable in split extensions of finitely generated free groups by virtually inner automorphisms. An algorithm for construction of…
We give a precise definition of ``generic-case complexity'' and show that for a very large class of finitely generated groups the classical decision problems of group theory - the word, conjugacy and membership problems - all have…
Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented non-free groups, with a particular emphasis…
We consider pairs of finitely presented, residually finite groups $P\hookrightarrow\G$ for which the induced map of profinite completions $\hat P\to \hat\G$ is an isomorphism. We prove that there is no algorithm that, given an arbitrary…
There exist combable groups in which the conjugacy problem is unsolvable. The isomorphism problem is unsolvable for certain recursive sequences of finite presentations of combable groups.
This paper initiates the study of effective twisted conjugacy separability for finitely generated groups, which measures the complexity of separating distinct twisted conjugacy classes via finite quotients. The focus is on nilpotent groups,…
Weanalyzethecomputationalcomplexityofanalgorithmtosolve the conjugacy search problem in a certain family of metabelian groups. We prove that in general the time complexity of the conjugacy search problem for these groups is at most…
We describe an effective version of the conjugacy problem and study it for wreath products and free solvable groups. The problem involves estimating the length of short conjugators between two elements of the group, a notion which leads to…
We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation in the sense of Borel reducibility.
We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.
Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…
Decision problems are problems of the following nature: given a property P and an object O, find out whether or not the object O has the property P. On the other hand, witness problems are: given a property P and an object O with the…
There is a natural equivalence relation on representations of the states of a given quantum system in a Hilbert space, two representations being equivalent iff they are related by a unitary transformation. There are two equivalence classes,…
A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.