Abstract
Addition sets with parameters ( υ, k, λ, α) are defined in a finite group G of order υ, where α: G → G is a homomorphism or anti-homomorphism. It is shown that addition sets in a finite group have similar properties to that of ( υ, k, λ, g) cyclic addition sets. The case α = I, where I: G → G is the identity automorphism, is studied and it is shown that no ( υ, k, λ, I) group addition sets exist in an Abelian group of order υ, where ether υ is odd, υ≡2 (mod 4), or in certain cases when υ≡0 (mod 4). Many examples of group addition sets in both Abelian and non-Abelian groups are provided.
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