Divisible difference set for a subgroup

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Definition

Let G be a finite group of order mn and N be a subgroup of G of order m. Then we say that a subset D of G is a divisible difference set with exceptional subgroup N if there are constants \lambda_1 and \lambda_2 such that:

  • Every non-identity element of N can be expressed as a right quotient of elements in D in exactly \lambda_1 ways.
  • Every element in G \setminus N can be expressed as a right quotient of elements in D in exactly \lambda_2 ways.