ISOMORPHISM THEOREMS FOR GYROGROUPS AND L-SUBGYROGROUPS

By Teerapong Suksumran, Keng Wiboonton. 2014

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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.

Subfields: Electrical and Electronic Engineering, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/b41031e1903b25a90975fac68b133c10a2946206