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Given a group G with generators ∆, it is well-known that the set of color-preserving automorphisms of the Cayley color digraph Γ = Cay ∆ (G) is isomorphic to G. Many people have studied the question of when the full automorphism group of the Cayley digraph is isomorphic to G. This paper explores what happens when the full automorphism group of G is not(More)
Goldman and Turaev constructed a Lie bialgebra structure on the free Z-module generated by free homotopy classes of loops on a surface. Turaev conjectured that his cobracket ∆(α) is zero if and only if α is a power of a simple class. Chas constructed examples that show Turaev's conjecture is, unfortunately, false. We define an operation µ in the spirit of(More)
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