The Whitehead Algorithm for free groups

Master's Thesis from the year 2013 in the subject Mathematics - Algebra, grade: -, University of Warwick (Institute of Mathematics), course: M.Sc dissertation in Pure Mathematics, language: English, abstract: We start with a brief introduction to Free Groups, thereby appreciating Nielsen¿s approach to the

Subgroup theorem. Beautiful results of J. H. C. Whitehead, J. Nielsen, E. S. Rapaport, Higgins and

Lyndon, and J. McCool form our building block. We study different automorphisms of a finitely generated

free group as well as a finite set of automorphisms which Whitehead used to deduce that if two elements

of a finitely generated free group are equivalent under an automorphism of the group, then they are

equivalent under such automorphisms. We write program aimed at appreciating Whitehead¿s theorem,

starting with programs for appreciating Whitehead automorphisms to programs for determining whether

two elements of a finitely generated free group are equivalent or not. We conclude by classifying all

minimal words of lengths 2, 3, 4, 5 and 6 in F n (for some n ¿ [2, 6]) up to equivalence.