The Brauer character of a finite-dimensional modular representation determines its semisimplification. More strongly, the irreducible Brauer characters are linearly independent as complex-valued functions on the p-regular conjugacy classes.
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The Brauer–Nesbitt theorem is a result in the theory of representations of finite groups, specifically pertaining to the representation theory of the symmetric group. The theorem characterizes the irreducible representations of a symmetric group \( S_n \) in terms of their behavior with respect to certain arithmetic functions.