Geodesic
On a class of weakly semi-abelian polyadic groups
Diskretnaya Matematika, Tome 8 (1996) no. 3, pp. 40-46 
W. A. Dudek. On a class of weakly semi-abelian polyadic groups. Diskretnaya Matematika, Tome 8 (1996) no. 3, pp. 40-46. http://geodesic.mathdoc.fr/item/DM_1996_8_3_a3/
@article{DM_1996_8_3_a3,
     author = {W. A. Dudek},
     title = {On a class of weakly semi-abelian polyadic groups},
     journal = {Diskretnaya Matematika},
     pages = {40--46},
     year = {1996},
     volume = {8},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1996_8_3_a3/}
}
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This work is devoted to the study of $m$-semiabelian $n$-ary Dörnte groups. Properties of such groups are considered, and necessary and sufficient conditions for an $n$-ary group to be weakly $m$-semiabelian are found. It is proved that for all $m\ge 3$ there exist primitive (i.e., irreducible) weakly semiabelian $n$-ary groups.