# Divisible difference set for a subgroup

From Groupprops

## Definition

Let be a finite group of order and be a subgroup of of order . Then we say that a subset of is a **divisible difference set** with **exceptional subgroup** if there are constants and such that:

- Every non-identity element of can be expressed as a right quotient of elements in in exactly ways.
- Every element in can be expressed as a right quotient of elements in in exactly ways.