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| 512.54+512.548 (3) |
| Algebra (400) |
 SM ISO690:2012GORKUNOV, Evgeny, KROTOV, Denis, POTAPOV, Vladimir. On the number of autotopies of an n-ary quasigroup of order 4. In: Quasigroups and Related Systems, 2019, vol. 27, nr. 2(42), pp. 227-250. ISSN 1561-2848. |
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 Quasigroups and Related Systems |
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| Volumul 27, Numărul 2(42) / 2019 / ISSN 1561-2848 | ||||||
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| CZU: 512.54+512.548 | ||||||
| Pag. 227-250 | ||||||
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An algebraic system consisting of a nite set of cardinality k and an n-ary operation f invertible in each argument is called an n-ary quasigroup of order k. An autotopy of an n-ary quasigroup (; f) is a collection (0; 1; : : : ; n) of n + 1 permutations of such that f(1(x1); : : : ; n(xn)) 0(f(x1; : : : ; xn)). We show that every n-ary quasigroup of order 4 has at least 2[n=2]+2 and not more than 6 4n autotopies. We characterize the n-ary quasigroups of order 4 with 2(n+3)=2, 2 4n, and 6 4n autotopies. |
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