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ABOUT TRIMEDIAL QUASIGROUPS Borzunova T.L. Chernomirdin 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 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 uv = xu yv

Medial quasigroups naturally it is possible to generalize as follows: The quasigroup Q() refers to trimedial, if its (her) any three elements derivate medial quasigroup. For example, distributive quasigroup, CH - quasigroup is a medial quasigroups. CH - quasigroups, trimedial quasigroups, In work communication (connection) commutative F - quasigroups is underlined. It appears, that in commutative F - quasigroup Q() the set of local units forms edinal e(Q) which coincides with associator Q() , 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.2728. 2. Belousov V.D. The bases of the quasigroup theory and loop - .: Science, 1967. 223 pages 3. Belousov V.D. The algebraic networks and quasigroups. - Chishinew: Shtiintsa, 1971. 165 pages.