Relative difference set for a subgroup

This term is related to: incidence geometry
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Definition

A subset $D$ of a group $G$ is termed a relative difference set with forbidden subgroup $N$ if:

• No non-identity element of $N$ can be expressed as a right quotient of elements of $D$
• Every element outside $N$ can be expressed as a right quotient of elements of $D$ in exactly $\lambda$ ways where $\lambda$ is a constant independent of the choice of element

Related notions

• Difference set
• Divisible difference set for a subgroup