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