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Hadamard Difference Sets in Nonabelian 2-Groups with High Exponent

Davis, James; Iiams, Joel


Keyword(s): difference set; nonabelian group; representation theory

Abstract: Nontrivial difference sets in groups of order a power of 2 are part of the family of difference sets called Hadamard difference sets. In the abelian case, the exponent of the group completely determines whether the group supports a Hadamard difference set. Recently, a nonabelian example was constructed which exceeded the (abelian) exponent bound. This paper extends that result to demonstrate that the asymptotic behavior of nonabelian groups is different than that of abelian groups.

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