Title of article
Classification of gyrogroups of orders at most 31
Author/Authors
Ashrafi ، Ali Reza Department of Pure Mathematics - Faculty of Mathematical Sciences - University of Kashan , Mavaddat Nezhaad ، Kurosh Department of Pure Mathematics - Faculty of Mathematical Sciences - University of Kashan , Salahshour ، Mohammad Ali Department of Mathematics - Islamic Azad University, Savadkooh Branch
From page
11
To page
18
Abstract
A gyrogroup is defined as having a binary operation containing an identity element such that each element has an inverse. Furthermore, for each pair (a,b) of elements of this structure, there exists an automorphism gyr[a,b] with the property that left associativity and the left loop property are satisfied. Since each gyrogroup is a left Bol loop, some results of Burn imply that all gyrogroups of orders p,2p, and p2, where p is a prime number, are groups. This paper aims to classify gyrogroups of orders 8, 12, 15, 18, 20, 21, and 28.
Keywords
Gyrogroup , left Bol loop , gyroautomorphism
Journal title
AUT Journal of Mathematics and Computing
Journal title
AUT Journal of Mathematics and Computing
Record number
2757825
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