Isomorphism Theorems for Gyrogroups and L-Subgyrogroups

We extend well-known results in group theory to gyrogroups, the isomorphism theorems. We prove that an gyrogroup G induces the gyrogroup structure on the group of G so that Cayley's Theorem is obtained. the notion of L-subgyrogroups, we show that an-subgyrogroup partitions G into left cosets. Consequently, if H an L-subgyrogroup of a finite gyrogroup G, then the order of divides the order of G.