Construction of new gyrogroups and the structure of their subgyrogroups

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 left 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 ۲-gyrogroups of order ۲^n, n\geq ۳, are presented. Some open questions are also proposed.

Keywords:

Gyrogroup , subgyrogroup , groupoid