# Commutator theory for congruence modular varieties

@article{Freese1989CommutatorTF, title={Commutator theory for congruence modular varieties}, author={Ralph Freese and Ralph McKenzie}, journal={Journal of Symbolic Logic}, year={1989}, volume={54}, pages={1114-1115} }

Introduction In the theory of groups, the important concepts of Abelian group, solvable group, nilpotent group, the center of a group and centraliz-ers, are all defined from the binary operation [x, y] = x −1 y −1 xy. Each of these notions, except centralizers of elements, may also be defined in terms of the commutator of normal subgroups. The commutator [M, N] (where M and N are normal subgroups of a group) is the (normal) subgroup generated by all the commutators [x, y] with x ∈ M, y ∈ N…

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