Construction of New Gyrogroups and the Structure of their Subgyrogroups

Abstract

Suppose that $G$ is a groupoid with binary operation $\otimes$. The pair $(G,\otimes )$ is said to be a gyrogroup if the operation $\otimes$ has a left identity, each element $a\in G$ has a left inverse and the gyroassociative law and the left loop property are satisfied in $G$. In this paper, a method for constructing new gyrogroups from old ones is presented and the structure of subgyrogroups of these gyrogroups are also given. As a consequence of this work, five $2-$gyrogroups of order $2^n$, $n\ge 3$, are presented. Some open questions are also proposed.

15 pages

References in corpus (1)

• Isomorphism Theorems for Gyrogroups and L-Subgyrogroups