The Whitehead Algorithm for free groups

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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 theSubgroup theorem. Beautiful results of J. H. C. Whitehead, J. Nielsen, E. S. Rapaport, Higgins andLyndon, and J. McCool form our building block. We study different automorphisms of a finitely generatedfree group as well as a finite set of automorphisms which Whitehead used to deduce that if two elementsof a finitely generated free group are equivalent under an automorphism of the group, then they areequivalent under such automorphisms. We write program aimed at appreciating Whitehead’s theorem,starting with programs for appreciating Whitehead automorphisms to programs for determining whethertwo elements of a finitely generated free group are equivalent or not. We conclude by classifying allminimal words of lengths 2, 3, 4, 5 and 6 in F n (for some n ∈ [2, 6]) up to equivalence.