On autotopies and automorphisms of n-ary linear quasigroups
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....
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| Date: | 2004 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2004
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/156416 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
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