Abstract
Two non-isomorphic finite groups form a Brauer pair if there exist a bijection for the conjugacy classes and a bijection for the irreducible characters that preserve all the character values and the power map. A group is called a VZ-group if all its nonlinear irreducible characters vanish off the center. In this paper we give necessary and sufficient conditions for two non-isomorphic VZ-groups to form a Brauer pair.
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