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Algebra Discrete Math., 2003, Issue 3, Pages 54–81 (Mi adm384)  

This article is cited in 1 scientific paper (total in 1 paper)

Gyrogroups and left gyrogroups as transversals of a special kind

Eugene Kuznetsov

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, str., Academiei, 5, MD–2028, Chishinau, MOLDOVA

Abstract: In this article we study gyrogroups and left gyrogroups as transversals in some suitable groups to its subgroups. These objects were introduced into consideration in a connection with an investigation of analogies between symmetries in the classical mechanics and in the relativistic one. The author introduce some new notions into consideration (for example, a weak gyrotransversal) and give a full description of left gyrogroups (and gyrogroups) in terms of transversal identities. Also he generalize a construction of a diagonal transversal and obtain a set of new examples of left gyrogroups.

Keywords: loop, group, transversal, automorphism, gyrogroup.

Full text: PDF file (267 kB)

Bibliographic databases:
MSC: 20N05, 20N15
Received: 15.06.2003
Revised: 04.11.2003
Language:

Citation: Eugene Kuznetsov, “Gyrogroups and left gyrogroups as transversals of a special kind”, Algebra Discrete Math., 2003, no. 3, 54–81

Citation in format AMSBIB
\Bibitem{Kuz03}
\by Eugene~Kuznetsov
\paper Gyrogroups and left gyrogroups as transversals of a~special kind
\jour Algebra Discrete Math.
\yr 2003
\issue 3
\pages 54--81
\mathnet{http://mi.mathnet.ru/adm384}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2048640}
\zmath{https://zbmath.org/?q=an:1067.20084}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sonmez N., Ungar A.A., “The Einstein Relativistic Velocity Model of Hyperbolic Geometry and its Plane Separation Axiom”, Adv. Appl. Clifford Algebr., 23:1 (2013), 209–236  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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