Geodesic
Gyrogroups and left gyrogroups as transversals of a~special kind
Algebra and discrete mathematics, no. 3 (2003), pp. 54-81

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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
Mots-clés : group, transversal, automorphism, gyrogroup. 
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     author = {Eugene Kuznetsov},
     title = {Gyrogroups and left gyrogroups as transversals of a~special kind},
     journal = {Algebra and discrete mathematics},
     pages = {54--81},
     publisher = {mathdoc},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2003_3_a3/}
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Eugene Kuznetsov. Gyrogroups and left gyrogroups as transversals of a~special kind. Algebra and discrete mathematics, no. 3 (2003), pp. 54-81. http://geodesic.mathdoc.fr/item/ADM_2003_3_a3/