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Turkish Journal of Mathematics

DOI

10.3906/mat-0805-2

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.

First Page

293

Last Page

304

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Mathematics Commons

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