Geodesic
Semi-commutativity criteria and self-coincidence elements expressed by vectors properties of $n$-ary groups
Algebra and discrete mathematics, Tome 9 (2010) no. 2, pp. 98-107.

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In this paper new criteria of semi-commutativity and results on self-coincidence of an arbitrary point $P$ in the terms of properties of vectors of $n$-ary groups are obtained.
Keywords: Semi-abelian $n$-ary group, self-coincidence of points (elements), symmetric points, a parallelogram of an $n$-ary group, vectors of $n$-ary groups. 
@article{ADM_2010_9_2_a6,
     author = {Yu. I. Kulazhenko},
     title = {Semi-commutativity criteria and self-coincidence  elements expressed by vectors properties of $n$-ary groups},
     journal = {Algebra and discrete mathematics},
     pages = {98--107},
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     volume = {9},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2010_9_2_a6/}
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Yu. I. Kulazhenko. Semi-commutativity criteria and self-coincidence  elements expressed by vectors properties of $n$-ary groups. Algebra and discrete mathematics, Tome 9 (2010) no. 2, pp. 98-107. http://geodesic.mathdoc.fr/item/ADM_2010_9_2_a6/