Construction of new gyrogroups and the structure of their subgyrogroups
Suppose that G is a groupoid with binary operation ⊗. The pair (G,⊗) is said to be a gyrogroup if the operation ⊗ has a left identity, each element a∈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 2−gyrogroups of order 2n, n≥3, are presented. Some open questions are also proposed.
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