On autotopies and automorphisms of n-ary linear quasigroups

• Published in: Algebra and Discrete Mathematics
• Date: 2004
• Main Authors: Marini, A., Shcherbacov, V.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2004
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/156416
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.