# Schur index of irreducible character in characteristic zero divides exponent

From Groupprops

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).

View other divisor relations |View congruence conditions

## Statement

Suppose is a finite group, is an Irreducible linear representation (?) of over , and is the Schur index (?) of . Then, divides the exponent of .

Here, can be replaced by any splitting field for of characteristic zero.