Abstract
Let\(\mathbb{S}_n \) be a symmetric group on a set {1,2,...,n}. For an arbitrary permutation π of\(\mathbb{S}_n \), we consider a variety n G π ofn-groupoids (A, f) satisfying the identityf(x 1,x 2,...,x n )=f(x π(1),x π(2)...,x π(n)). It is proved that if lengths of all independent cycles of π are positive degrees of one numberm ≥2 then n G π has a finite dimension equal to the number of prime divisors ofm. The dimension of a variety, in this event, is the least upper bound of lengths of independent bases for the collection of all strong Mal’tsev conditions satisfied in that variety.
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