On Schreier Varieties of n-Groups and n-Semigroups

Equations in polyadic groups

“…Russian reader, can use the book of Galmak [18], for an almost complete description of polyadic groups. The articles [2], [12], [19], and [20] can be used for study of axioms of polyadic groups as well as their varieties.…”

“…Varieties of polyadic groups and the structure of congruences on polyadic groups are studied in [2] and [12]. It is proved that all congruences on polyadic groups are commute and so the lattice of congruences is modular.…”

Simple polyadic groups

“…Reader who knows Russian, can use the book of Galmak [11], for an almost complete description of polyadic groups and as we understand from its English abstract, some of our results are also proved in that book by a different method. The articles [1], [4], [12], and [13] can be used for study of axioms of polyadic groups as well as their varieties.…”

“…Varieties of polyadic groups and the structure of congruences on polyadic groups are studied in [1], [4] and [22]. It is proved that all congruences on polyadic groups are commute and so the lattice of congruences is modular.…”

“…. , a n , b ∈ G and 1 ≤ i ≤ n, there exists a unique element x ∈ G such that f (a i− 1 1 , x, a n i+1 ) = b. It is proved that the uniqueness assumption on the solution x can be dropped, see [5] for details.…”