Abstract:

According to difference set and difference set pairs multiplier theorem and multiplier conjecture, the method by onorbit can determine the nonexistence of difference set and difference set pairs. The orbit created by prime p in Abelian group G by order v is discussed. Two kinds of orbit discipline are presented and proved. The one is order described by only one prime number, another is order described by the product of two prime numbers. Nonexistence of difference set or difference set pairs with the specific parameters is determined.

Key words: difference set, difference set pairs, multiplier theorem, multiplier conjecture, orbit