A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d1d2-1 : d1, d2D, d1d2} contains each nonidentity element of G exactly λ times. A difference set is called abelian, nonabelian or cyclic according to the properties of the underlying group. Difference sets are important in design theory because they are equivalent to symmetric (v, k, λ) designs with a regular automorphism group [L].

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Copyright © 1996 Walter de Gruyter. This chapter first appeared in Groups, Difference Sets, and the Monster: Proceedings of a Special Research Quarter at the Ohio State University, Spring 1993.

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