Finite subquandles of sphere

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(Q1) and G(Q2) of O(3) are isomorphic by which finite subquandles of sphere are classified.