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 $m = 2$.

Keywords

n-Ary group / Identity / m-Neutral sequence

References

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