In group theory, the commutator \([x,y]\) induces a binary operation on the lattice of normal subgroups, which is used to define the important concepts of abelian group, solvable group, nilpotent group, etc. Together with the lattice operations, the commutator thus carries much of the information of the structure of a group. In this talk we will define a commutator for congruence lattices of general algebras and study some basic properties of the operation.
A general commutator