Automorphism groups of Quandles

Abstract

We prove that the automorphism group of the dihedral quandle with n elements is isomorphic to the affine group of the integers mod n, and also obtain the inner automorphism group of this quandle. In [9], automorphism groups of quandles (up to isomorphisms) of order less than or equal to 5 were given. With the help of the software Maple, we compute the inner and automorphism groups of all seventy three quandles of order six listed in the appendix of [4]. Since computations of automorphisms of quandles relates to the problem of classification of quandles, we also describe an algorithm implemented in C for computing all quandles (up to isomorphism) of order less than or equal to nine.

References in corpus (1)

• Automorphism groups of Quandles

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• Minimal sufficient sets of colors and minimum number of colors
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• Reflections to set-theoretic solutions of the Yang-Baxter equation
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• The Delunification Process and Minimal Diagrams
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