# Conjugacy classes

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G is a finite group with elements a and b. Let the conjugacy classes of these elements be A and B respectively and suppose |A|^2, |B|^2 < |G|. Prove that there is a non-identity element x in G s.t. x commutes with both a and b.

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#### Solution Summary

This is a proof regarding conjugacy classes and a non-identity element.

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