Geodesic
On semicenters of $l$-ary groupoids
Problemy fiziki, matematiki i tehniki, no. 2 (2013), pp. 76-80

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In the paper the author continues to describe his research dedicated to the study of the properties of the $l$-ary groupoid $\langle A^J, [\,]_{l,\sigma,J}\rangle$ where $A^J$ is a set of all mappings of an arbitrary set $J$ in an arbitrary groupoid $A$, and the $l$-ary operation $[\,]_{l,\sigma,J}$ is defined for any integer $l\geqslant 2$ and for any permutation $\sigma$ of the set $J$. In particular, some semiabelian criteria of this $l$-ary groupoid are found.
Keywords: $n$-ary group, $l$-ary groupoid, semiabelity, $l$-ary operation. 
@article{PFMT_2013_2_a10,
     author = {Yu. I. Kulazhenko},
     title = {On semicenters of $l$-ary groupoids},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {76--80},
     publisher = {mathdoc},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2013_2_a10/}
}
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Yu. I. Kulazhenko. On semicenters of $l$-ary groupoids. Problemy fiziki, matematiki i tehniki, no. 2 (2013), pp. 76-80. http://geodesic.mathdoc.fr/item/PFMT_2013_2_a10/