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IMCS/Publications/QRS/Issues/QRS v.13, n.1 (13), 2005/

Finite n-ary medial quasigroups and its automorphism

Authors: Şcerbacov Victor

Abstract

We prove that any finite medial n-ary quasigroup is isomorphic to the direct product of a medial unipotently-solvable quasigroup and a principal isotope of a medial idempotent quasigroup. For binary case similar theorem was proved by D.C. Murdoch. This theorem gives a possibility to obtain information on automorphism groups of finite n-ary medial quasigroups.

V.A.Shcherbacov
Institute of Mathematics
and Computer Science
Academy of Sciences of Moldova
Academiei 5, MD-2028
Moldova.
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