On autotopies and automorphisms of \(n\)-ary linear quasigroups
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 quasi...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/991 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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. |
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