On Identities and m-Neutral Sequences of n-Ary Groups

Abstract

In this paper, we study such polyadic analog of an identity of a group as m-neutral sequence. In particular, we prove that all Post’s equivalence classes of the free covering group of any n-ary group [where \(n = k(m - 1) + 1\) and \(k\ge 1\)] defined by m-neutral sequences form the \((k + 1)\)-ary group, which is isomorphic to the n-ary subgroup of all identities of the n-ary group in the case when \(m = 2\).