This article is cited in 2 papers

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.

MSC: 20N05, 20N15

Received: 15.06.2003
Revised: 04.11.2003

Language: English

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