Journals / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 2
Finite subquandles of sphere
- Pages
- 293–303
- DOI
- —
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 GQ of O(3) associated with Q. It is shown that if Q is a finite (infinite) subquandle, then GQ 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 Q1 and Q2 of sphere whose all elements are not on the same great circle are isomorphic if and only if the subgroups GQ1 and GQ2 of O(3) are isomorphic by which finite subquandles of sphere are classified.
Özet
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 GQ of O(3) associated with Q. It is shown that if Q is a finite (infinite) subquandle, then GQ 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 Q1 and Q2 of sphere whose all elements are not on the same great circle are isomorphic if and only if the subgroups GQ1 and GQ2 of O(3) are isomorphic by which finite subquandles of sphere are classified.