Many aspects of defect theorems

We give a survey and a unified presentation of the defect theorem, its generalizations and recent aspects of interest. In its basic form, the defect theorem states that if a set of n words satisfies a nontrivial relation, then these words can be expressed simultaneously as products of at most n - 1 words. In other words, dependency of words causes a defect effect. There does not exist just one defect theorem, but several ones depending on the restrictions that are put to the n - 1 words. The defect theorem is closely related to equations of words, and in this way to the compactness theorem for systems of word equations.

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