Geodesic
One approach to constructing a~transitive class of block transformations
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 27-29

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Let $\Omega$ be an arbitrary finite set, and $\mathcal Q(\Omega)$ be the collection of all the binary quasigroups defined on the set $\Omega$. Denote by $\Sigma^F$ the map $\Omega^n\to\Omega^n$, $n\in\mathbb N$, that is defined by the network $\Sigma$ with one binary operation $F$ on the set $\Omega$. In this paper, we present a criterion for the bijectivity of all mappings from the class $\{\Sigma^F\colon F\in\mathcal Q(\Omega)\}$ and define conditions for the transitivity of this class.
Keywords: network
Mots-clés : quasigroup. 
@article{PDMA_2017_10_a9,
     author = {I. V. Cherednik},
     title = {One approach to constructing a~transitive class of block transformations},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {27--29},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a9/}
}
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I. V. Cherednik. One approach to constructing a~transitive class of block transformations. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 27-29. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a9/