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.
Keywords
Quandle, orthogonal group.
First Page
293
Last Page
304
Recommended Citation
ÖZDEMİR, NÜLİFER and AZCAN, HÜSEYİN
(2010)
"Finite subquandles of sphere,"
Turkish Journal of Mathematics: Vol. 34:
No.
2, Article 12.
https://doi.org/10.3906/mat-0805-2
Available at:
https://journals.tubitak.gov.tr/math/vol34/iss2/12
