Schur index of irreducible character in characteristic zero divides exponent

From Groupprops
Jump to: navigation, search
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


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.

Related facts