On structure of finite n-ary medial quasigroups and automorphism groups of these quasigroups
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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

On structure of finite n-ary medial quasigroups and automorphism groups of these quasigroups

Pag. 125-156

Shcherbacov Victor
 
 
 
Disponibil în IBN: 14 decembrie 2013


Rezumat

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.