1. Classification of gyrogroups of orders at most 31.
- Author
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Ashrafi, Ali Reza, Nezhaad, Kurosh Mavaddat, and Salahshour, Mohammad Ali
- Subjects
AUTOMORPHISMS ,PRIME numbers ,INVERSE functions ,ASSOCIATIVITY (Propositional logic) ,BINARY operations - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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