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arXiv · 1406.0300

Isomorphism Theorems for Gyrogroups and L-Subgyrogroups

Teerapong Suksumran·Keng Wiboonton
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Abstract

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 $G$.

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Teerapong Suksumran, Keng Wiboonton. 2014-11-05. Isomorphism Theorems for Gyrogroups and L-Subgyrogroups. https://doi.org/10.7546/jgsp-37-2015-67-83

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