Variety of loops is congruence-uniform

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The variety of loops is a congruence-uniform variety. In other words, every loop is a congruence-uniform algebra in the variety of loops. More explicitly, given any loop and a congruence on it, the congruence classes are of equal size.

Translation to the language of groups

In the language of groups, the above statement interprets as: all the cosets of a normal subloop are of the same size and form a partition of the underlying set of the loop.

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