# 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}
}```
• Published 1 September 1989
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• Journal of Symbolic Logic
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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