Soheila Mahdavi - Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan ۸۷۳۱۷-۵۳۱۵۳, I. R. Iran
Ali Ashrafi - Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan ۸۷۳۱۷-۵۳۱۵۳, I. R. Iran.
Mohammad Salahshour - Department of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, I. R. Iran

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.

Gyrogroup, subgyrogroup, groupoid