Geodesic
On autotopies and automorphisms of $n$-ary linear quasigroups
Algebra and discrete mathematics, no. 2 (2004), pp. 59-83.

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In this article we study structure of autotopies, automorphisms, autotopy groups and automorphism groups of $n$-ary linear quasigroups. We find a connection between automorphism groups of some special kinds of $n$-ary quasigroups (idempotent quasigroups, loops) and some isotopes of these quasigroups. In binary case we find more detailed connections between automorphism group of a loop and automorphism group of some its isotope. We prove that every finite medial $n$-ary quasigroup of order greater than 2 has a non-identity automorphism group. We apply obtained results to give some information on automorphism groups of $n$-ary quasigroups that correspond to the ISSN code, the EAN code and the UPC code.
Keywords: $n$-ary quasigroup, $n$-ary T-quasigroup, isotopy, autotopy.
Mots-clés : quasigroup, automorphism, medial quasigroup 
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     title = {On autotopies and automorphisms of $n$-ary linear quasigroups},
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     year = {2004},
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     url = {http://geodesic.mathdoc.fr/item/ADM_2004_2_a7/}
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Alberto Marini; Victor Shcherbacov. On autotopies and automorphisms of $n$-ary linear quasigroups. Algebra and discrete mathematics, no. 2 (2004), pp. 59-83. http://geodesic.mathdoc.fr/item/ADM_2004_2_a7/