aequationes mathematicae

, Volume 56, Issue 1–2, pp 11–17 | Cite as

On the notion of gyrogroup

  • L. V. Sabinin
  • L. L. Sabinina
  • L. V. Sbitneva


It is shown that the gyrogroup [1] is just the well known left Bol loop with Bruck identity. This result has been announced in [12]. The other constructions of [1] are also discussed.

Keywords. Loop, quasigroup, gyrogroup, Bol identity, Lobachevski space. 


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Copyright information

© Birkhäuser-Verlag 1998

Authors and Affiliations

  • L. V. Sabinin
    • 1
  • L. L. Sabinina
    • 2
  • L. V. Sbitneva
    • 3
  1. 1.Department of Mathematics, Friendship of Nations University, Moscow 117198, Russia Russia
  2. 2.School of Mathematics and Physics, University of Michoacan, Morelia, Mexico, e-mail: sabinina@zeus.ccu.umich.mxMexico
  3. 3.Department of Mathematics, Moscow Institute of Electronics and Mathematics, Moscow 109028, RussiaRussia

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