Эта публикация цитируется в
9 статьях
RESEARCH ARTICLE
On autotopies and automorphisms of $n$-ary linear quasigroups
Alberto Marinia,
Victor Shcherbacovb a Institute for Applied Mathematics
and Information Technologies of CNR, Via E. assini, 15, I–20133
Milano, Italy
b Institute of Mathematics and Computer Science,
Academy of Sciences of Moldova, str. Academiei, 5, MD–2028 Chişinău, Moldova
Аннотация:
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.
Ключевые слова:
quasigroup, automorphism,
$n$-ary quasigroup, medial quasigroup,
$n$-ary T-quasigroup, isotopy, autotopy.
MSC: 20N15,
20N05 Поступила в редакцию: 20.02.2004
Исправленный вариант: 28.05.2004
Язык публикации: английский
Полный текст:
PDF файл (308 kB)