Open Access
2015 Isomorphism Theorems for Gyrogroups and L-Subgyrogroups
Teerapong Suksumran, Keng Wiboonton
J. Geom. Symmetry Phys. 37: 67-83 (2015). DOI: 10.7546/jgsp-37-2015-67-83


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. "Isomorphism Theorems for Gyrogroups and L-Subgyrogroups." J. Geom. Symmetry Phys. 37 67 - 83, 2015.


Published: 2015
First available in Project Euclid: 27 May 2017

zbMATH: 1318.20060
MathSciNet: MR3362496
Digital Object Identifier: 10.7546/jgsp-37-2015-67-83

Rights: Copyright © 2015 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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