Abstract
Given the congruence lattice \({{\mathbb{L}}}\) of a finite algebra A with a Mal’cev term, we look for those sequences of operations on \({{\mathbb{L}}}\) that are sequences of higher commutator operations of expansions of A. The properties of higher commutators proved so far delimit the number of such sequences: the number is always at most countably infinite; if it is infinite, then \({{\mathbb{L}}}\) is the union of two proper subintervals with nonempty intersection.
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