@article {
author = {Suksumran, Teerapong},
title = {Special Subgroups of Gyrogroups: Commutators, Nuclei and Radical},
journal = {Mathematics Interdisciplinary Research},
volume = {1},
number = {1},
pages = {53-68},
year = {2016},
publisher = {University of Kashan},
issn = {2476-4965},
eissn = {2476-4965},
doi = {10.22052/mir.2016.13907},
abstract = {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.},
keywords = {Gyrogroup,Commutator subgyrogroup,nucleus of gyrogroup,subgyrogroup of prime index,radical of gyrogroup},
url = {https://mir.kashanu.ac.ir/article_13907.html},
eprint = {https://mir.kashanu.ac.ir/article_13907_7d64c578f99c83315fe22b9317d61813.pdf}
}