On central difference sets in certain non-abelian 2-groups

  • Authors:

  • Rod Gow;Rachel Quinlan

  • Affiliations:

  • Mathematics Department, University College, Belfield, Dublin, Ireland;Mathematics Department, University College, Belfield, Dublin, Ireland

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2006

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Abstract

In this note, we define the class of finite groups of Suzuki type, which are non-abelian groups of exponent 4 and class 2 with special properties. A group G of Suzuki type with |G| = 22s always possesses a non-trivial difference set. We show that if s is odd, G possesses a central difference set, whereas if s is even, G has no non-trivial central difference set.