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SM ISO690:2012 SHCHERBACOV, Victor. On structure of finite n-ary medial quasigroups and automorphism groups of these quasigroups
. In: Quasigroups and Related Systems, 2005, vol. 13, nr. 1(13), pp. 125-156. ISSN 1561-2848. |
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Quasigroups and Related Systems | ||||||
Volumul 13, Numărul 1(13) / 2005 / ISSN 1561-2848 | ||||||
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Pag. 125-156 | ||||||
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We prove that any nite 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 nite n-ary medial
quasigroups.
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