On autotopies and automorphisms of n-ary linear quasigroups

• Veröffentlicht in: Algebra and Discrete Mathematics
• Datum: 2004
• Hauptverfasser: Marini, A., Shcherbacov, V.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2004
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/156416
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: On autotopies and automorphisms of n-ary linear quasigroups / A. Marini, V. Shcherbacov // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 2. — С. 59–83. — Бібліогр.: 24 назв. — англ.

In this article we study structure of autotopies, automorphisms, autotopy groups and automorphism groups of nary 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 nonidentity 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.