Schur index of irreducible character in characteristic zero divides exponent

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This article states a result of the form that one natural number divides another. Specifically, the (Schur index) of a/an/the (irreducible linear representation) divides the (exponent of a group) of a/an/the (finite group).
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Statement

Suppose G is a finite group, \varphi is an Irreducible linear representation (?) of G over \mathbb{C}, and m(\chi) is the Schur index (?) of \chi. Then, m(\chi) divides the exponent of G.

Here, \mathbb{C} can be replaced by any splitting field for G of characteristic zero.

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