English

Automorphism groups of Quandles

Group Theory 2014-01-29 v1 Geometric Topology

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.

Keywords

Cite

@article{arxiv.1012.5291,
  title  = {Automorphism groups of Quandles},
  author = {M. Elhamdadi and J. MacQuarrie and R. Restrepo},
  journal= {arXiv preprint arXiv:1012.5291},
  year   = {2014}
}
R2 v1 2026-06-21T17:03:46.365Z