The structure of automorphic conjugacy in the free group of rank two.

Title: The structure of automorphic conjugacy in the free group of rank two.
Identifier: AAI3103124
identifier: 3103124
Creator: Khan, Bilal.
Contributor: Adviser: Alexei Miasnikov
Date: 2003
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: In the study of the automorphism group of a free group F = F(X) on a set X, J. H. C. Whitehead introduced a graph whose vertices are elements of F, where two vertices are connected if and only if the corresponding elements of F are related by one of a specially chosen set of generators of Aut(F). Here we give a structural description of Whitehead's graph for the case where F = F 2 is the free group of rank two. This description allows us to quantify relationships between the natural length function | | of F 2, and the action of Aut(F2) on F2. As an application, we devise the first known quadratic-time algorithm for testing automorphic conjugacy in F2.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.

Media: The structure of automorphic conjugacy in the free group of rank two.