A ug 2 00 5 On the Orbit Decomposition of Finite Quandles

  title={A ug 2 00 5 On the Orbit Decomposition of Finite Quandles},
  author={Sam Nelson and C. P. Wong},
We study the structure of finite quandles in terms of subquandles. Every finite quandle Q decomposes as a union of disjoint Q-complemented subquandles which coincide with the orbits of Q. Conversely, the structure of a quandle with a given orbit decomposition is determined by rack actions satisfying a compatibility condition. We include Maple code for finding orbit decompositions and quandle structures on disjoint unions of quandles. 

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