## Journal of Geometry and Symmetry in Physics

### Isomorphism Theorems for Gyrogroups and L-Subgyrogroups

#### 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 $G$.

#### Article information

Source
J. Geom. Symmetry Phys., Volume 37 (2015), 67-83.

Dates
First available in Project Euclid: 27 May 2017

https://projecteuclid.org/euclid.jgsp/1495850553

Digital Object Identifier
doi:10.7546/jgsp-37-2015-67-83

Mathematical Reviews number (MathSciNet)
MR3362496

Zentralblatt MATH identifier
1318.20060

#### Citation

Suksumran, Teerapong; Wiboonton, Keng. Isomorphism Theorems for Gyrogroups and L-Subgyrogroups. J. Geom. Symmetry Phys. 37 (2015), 67--83. doi:10.7546/jgsp-37-2015-67-83. https://projecteuclid.org/euclid.jgsp/1495850553