Special Subgroups of Gyrogroups: Commutators, Nuclei and Radical

Document Type : Special Issue: AIMC 51


Department of Mathematics, North Dakota State University, Fargo, ND 58105, USA


‎A gyrogroup is a nonassociative group-like structure modelled on the ‎space of relativistically admissible velocities with a binary ‎operation given by Einstein's velocity addition law‎. ‎In this ‎article‎, ‎we present a few of groups sitting inside a gyrogroup G‎, ‎including the commutator subgyrogroup‎, ‎the left nucleus‎, ‎and the ‎radical of G‎. ‎The normal closure of the commutator subgyrogroup‎, ‎the left nucleus‎, ‎and the radical of G are in particular normal ‎subgroups of G‎. ‎We then give a criterion to determine when a ‎subgyrogroup H of a finite gyrogroup G‎, ‎where the index ‎[G: H] is the smallest prime dividing |G|‎, ‎is normal in G‎.


Main Subjects

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