# Schur index of irreducible character is one in any prime characteristic

From Groupprops

## Contents

## Statement

Suppose is a prime number, is a finite group, and is the character of an an irreducible linear representation of in characteristic . Then, the Schur index (?) of is 1.

## Related facts

- Schur index of irreducible character in characteristic zero divides exponent
- Schur index divides degree of irreducible representation
- Odd-order p-group implies every irreducible representation has Schur index one

## Facts used

## Proof

The proof follows from the alternative characterization of Schur index in terms of division rings.