# Difference set

This term is related to: incidence geometry
View other terms related to incidence geometry | View facts related to incidence geometry
View other properties of subsets of groups|View properties of subsets of abelian groups|View subgroup properties

## Definition

A subset $D$ of a finite group $G$ is termed a difference set if every non-identity element of $G$ can be written as a right quotient of elements of $D$ in exactly $\lambda$ ways, for some fixed $\lambda$ independent of the choice of element.

## Terminology for difference sets

The order of a difference set is defined as the cardinality of the difference set, minus $\lambda$ where $\lambda$ is the number of ways of writing each non-identity element as a right quotient of elements of the difference set.

## Notions of equivalence

### Isomorphic difference sets

Two difference sets (in possibly different groups) ar esaid to be isomorphic if they define isomorphic designs.

### Equivalent difference sets

Two difference sets in a group are said to be equivalent if there is an automorphism of the group that maps one difference set to a translate of the other.