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Conference publicationsAbstractsXIX conferenceAbout trimedial quasigroupsChernomirdin Moscow State Open University , Faculty Applied Mathematics, Chair of Informatics and Information Technology,Pavel Corchagin st., 22, Moscow , 107996, Russia,Phone: 8(495) 683-68-46, e-mail: t.borzunova@yandex.ru , b_o_r@rambler.ru 2 pp. (accepted)The term ‘quasigroup’ was belongs to R.Mufang. Her works, denoted by non-desarg project plane, become push in development of the theory of quasigroup. At present, this theory of quasigroups is the separate section of the algebra. That section haves relations with: • the most algebra ; • the geometry (the theory projective planes); • the theory combinstoric (the theory latin square); • the algebraic networks and others. Medial quasigroup class is a one of the first classes that was a studied. These the quasigroups are defined (determined) by identity xy o uv=xu o yv Medial quasigroups naturally it is possible to generalize as follows: The quasigroup Q(o) refers to trimedial, if its (her) any three elements derivate medial quasigroup. For example, distributive quasigroup, CH- quasigroup is a medial quasigroups. In work communication (connection) CH -quasigroups, trimedial quasigroups, commutative F- quasigroups is underlined. It appears, that in commutativeF- quasigroupQ(o) the set of local units forms edinal e(Q) which coincides with associator Q(o), that is the factor - quasigroup Q/e(Q) is (commutative) group. And, that the class CH-quasigroups coincides with a class total - symmetric F- quasigroups.
References 1. Borzunova T.L. To the question about trimedial quasigroups.// Abstracts of the twelfth General Meeting of European Women in Mathematics (EWM).-Volgograd, VSU, 2005. Pp.27-28. 2. Belousov V.D. The bases of the quasigroup theory and loop - М.: Science, 1967. 223 pages 3. Belousov V.D. The algebraic networks and quasigroups. - Chishinew: Shtiintsa, 1971. 165 pages.
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