Turkish Journal of Mathematics
Abstract
In this work finite subquandles of sphere are classified by using classification of subgroups of orthogonal group O(3). For any subquandle Q of sphere there is a subgroup G_Q of O(3) associated with Q. It is shown that if Q is a finite (infinite) subquandle, then G_Q is a finite (infinite) subgroup. Finite subquandles of sphere are obtained from actions of finite subgroups of SO(3) on sphere. It is proved that the finite subquandles Q_1 and Q_2 of sphere whose all elements are not on the same great circle are isomorphic if and only if the subgroups G_{Q_1} and G_{Q_2} of O(3) are isomorphic by which finite subquandles of sphere are classified.
DOI
10.3906/mat-0805-2
Keywords
Quandle, orthogonal group.
First Page
293
Last Page
304
Recommended Citation
ÖZDEMİR, N, & AZCAN, H (2010). Finite subquandles of sphere. Turkish Journal of Mathematics 34 (2): 293-304. https://doi.org/10.3906/mat-0805-2
