|
Algebra and Discrete Mathematics, 2004, Issue 2, Pages 59–83
(Mi adm339)
|
|
|
|
This article is cited in 9 scientific papers (total in 9 papers)
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
Abstract:
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:
quasigroup, automorphism, $n$-ary quasigroup, medial quasigroup, $n$-ary T-quasigroup, isotopy, autotopy.
Received: 20.02.2004 Revised: 28.05.2004
Citation:
Alberto Marini, Victor Shcherbacov, “On autotopies and automorphisms of $n$-ary linear quasigroups”, Algebra Discrete Math., 2004, no. 2, 59–83
Linking options:
https://www.mathnet.ru/eng/adm339 https://www.mathnet.ru/eng/adm/y2004/i2/p59
|
Statistics & downloads: |
Abstract page: | 209 | Full-text PDF : | 82 | First page: | 1 |
|