Special Subgroups of Gyrogroups: Commutators, Nuclei and Radical

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چکیده مقاله:

‎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 ‎$[Gcolon H]$ is the smallest prime dividing |G|‎, ‎is normal in G‎.

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عنوان ژورنال

دوره 1  شماره 1

صفحات  53- 68

تاریخ انتشار 2016-01-01

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