Abstract
The main focus of this research paper is to investigate the properties of group completion within the framework of gyrogroups. Additionally, we establish a relationship between the category of groups and the category of gyrogroups, thereby providing a unified perspective on these two distinct mathematical structures.
This is a preview of subscription content, log in via an institution to check access.
Data availability
Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.
References
Ungar AA (2002) Beyond the Einstein addition law and its gyroscopic thomas precession: the theory of gyrogroups and gyrovector spaces. Springer, Amsterdam
Ungar AA (1997) Thomas precession: its underlying gyrogroup axioms and their use in hyperbolic geometry and relativistic physics. Found Phys 27(6):881–951
Ungar AA (2008) Analytic hyperbolic geometry and Albert Einstein's special theory of relativity. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ
Ungar AA (2016) The intrinsic beauty, harmony and interdisciplinarity in Einstein velocity addition law: gyrogroups and gyrovector space. Math Interdiscip Res 1(1):5–51
Foguel T, Ungar AA (2001) Gyrogroups and the decomposition of groups into twisted subgroups and subgroups. Pac J Math 197(1):1–11
Suksumran T, Wiboonton K (2014) Lagrange's theorem for gyrogroups and the Cauchy property. Quasigroups Relat Syst 22(2):283–294
Suksumran T, Wiboonton K (2015) Isomorphism theorems for gyrogroups and L-subgyrogroups. J Geom Symmetry Phys 37:67–83
Lal R, Singh AK (2014) Weak classification of finite groups. Asian-Eur J Math 7:1450058
Bussabun L, Kaewkhao A, Suantai S (2019) Cayley graphs of gyrogroups. Quasigroups Relat Syst 27:25–32
Acknowledgements
We are extremely thankful to Prof. Ramji Lal for his continuous support, discussion and encouragement. The first named authors thank IIIT Allahabad and Ministry of Education, Government of India for providing institute fellowship. The third named author is thankful to IIIT Allahabad for providing SEED grant.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The submitted work is original and has not been submitted or published elsewhere in any form or language (partially or in full). There is no conflict of interest regarding the article and every author has equally contributed.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kumar, A., Pandey, M.S., Kushwaha, S. et al. Group Completion of a Gyrogroup. Natl. Acad. Sci. Lett. (2024). https://doi.org/10.1007/s40009-024-01391-7
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40009-024-01391-7