# Lcm of Schur indices of irreducible representations

## Definition

### For a group over a field

Suppose is a group and is a field whose characteristic does not divide the order of . The **lcm of Schur indices of irreducible representations** of over is defined as the least common multiple of all the Schur index values of all the irreducible linear representations of over .

### Typical context: finite group and splitting field

The typical context is where is a finite group and is a splitting field for . In particular, the characteristic of is either zero or is a prime not dividing the order of , and every irreducible representation of over any extension field of can be realized over .