On a class of weakly semi-abelian polyadic groups

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.