# Weight for a finite group

## Contents

## Definition

### Definition with symbols

let be a prime and a finite group. A **weight** of is a pair such that:

- is a -subgroup of , and in fact, (viz it is the -Sylow core of its normalizer ).
- is an irreducible character of , the restriction of to is trivial, and belongs to a -block of of defect zero.

### Equivalence notion

Two weights are said to be equal if their is an inner automorphism of taking one to the other.

### Weights for a block

For a -block of , the weight is said to eb a -weight if where is the associated block on .