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- Title
AUTOMORPHISM GROUPS OF QUANDLES.
- Authors
ELHAMDADI, MOHAMED; MACQUARRIE, JENNIFER; RESTREPO, RICARDO; Hou, X.-D.
- 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 [B. Ho and S. Nelson, Matrices and finite quandles, Homology Homotopy Appl.7(1) (2005) 197-208.], 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 [S. Carter, S. Kamada and M. Saito, Surfaces in 4-Space, Encyclopaedia of Mathematical Sciences, Vol. 142, Low-Dimensional Topology, III (Springer-Verlag, Berlin, 2004)]. Since computations of automorphisms of quandles relate 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.
- Subjects
AFFINE algebraic groups; AUTOMORPHISMS; GROUP theory; ISOMORPHISM (Mathematics); ABSTRACT algebra; KNOT theory; MATHEMATICAL proofs
- Publication
Journal of Algebra & Its Applications, 2012, Vol 11, Issue 1, p1250008-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498812500089