DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in press


Authors:

T. Suksumran

Teerapong Suksumran

Department of Mathematics
Faculty of Science
Chiang Mai University
Chiang Mai 50200, Thailand

email: teerapong.suksumran@cmu.ac.th

0000-0002-1239-5586

Title:

A note on the gyrogroups of order 8

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Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2024-09-07 , Revised: 2024-12-21 , Accepted: 2024-12-22 , Available online: 2025-08-21 , https://doi.org/10.7151/dmgaa.1488

Abstract:

In this paper, we exhibit the complete list of gyrogroups of order 8 up to isomorphism. These gyrogroups will be used as examples or counter-examples to answer a few questions raised by some authors.

Keywords:

finite gyrogroup, normal subgyrogroup, strong subgyrogroup, $L$-subgyrogroup

References:

  1. A.R. Ashrafi, K.M. Nezhaad and M.A. Salahshour, Classification of \mbox{gyrogroups} of orders at most 31, AUT J. Math. Com. 5(1) (2024) 11–18.
    https://doi.org/10.22060/AJMC.2023.21939.1125
  2. R.P. Burn, Finite Bol loops, Math. Proc. Cambridge Philos. Soc. 84 (1978) 377–386.
    https://doi.org/10.1017/S0305004100055213
  3. H. Kiechle, Theory of {K}-loops (Springer-Verlag, Berlin, 2002).
  4. T. Suksumran, The algebra of gyrogroups: Cayley's theorem, Lagrange's \mbox{theorem}, and isomorphism theorems, Essays in mathematics and its applications (Th. M. Rassias and P.M. Pardalos, eds.) (2016), 369–437.
    https://doi.org/10.1007/978-3-319-31338-2\_15
  5. T. Suksumran, Special subgroups of gyrogroups: Commutators, nuclei and radical, Math. Interdiscip. Res. 1(1) (2016) 53–68.
    https://doi.org/10.22052/mir.2016.13907
  6. T. Suksumran, Involutive groups, unique 2-divisibility, and related \mbox{gyrogroup} structures, J. Algebra Appl. 16(6) (2017) Article ID 1750114.
    https://doi.org/10.1142/S0219498817501146
  7. T. Suksumran and A. A. Ungar, Gyrogroups and the Cauchy property, Quasigroups Related Systems 24(2) (2016) 277–286.
  8. T. Suksumran and K. Wiboonton, Lagrange's theorem for gyrogroups and the Cauchy property, Quasigroups Related Systems 22(2) (2014) 283–294.
  9. T. Suksumran and K. Wiboonton, Isomorphism theorems for \mbox{gyrogroups} and L-subgyrogroups, J. Geom. Symmetry Phys. 37 (2015) 67–83.
    https://doi.org/10.7546/jgsp-37-2015-67-83
  10. A. A. Ungar, Analytic Hyperbolic Geometry and Albert Einstein's Special Theory of Relativity (World Scientific, Hackensack, NJ, 2008).

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