Sequences of Commutator Operations
Erhard Aichinger, Nebojša Mudrinski · Order · 2013
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.