Difference Set - Multipliers

Multipliers

It has been conjectured that if p is a prime dividing and not dividing v, then the group automorphism defined by fixes some translate of D. It is known to be true for, and this is known as the First Multiplier Theorem. A more general known result, the Second Multiplier Theorem, first says to choose a divisor of . Then, with coprime t and v, fixes some translate of if for every prime p dividing m, there exists an integer i such that, where is the exponent (the least common multiple of the orders of every element) of the group.

For example, 2 is a multiplier of the (7,3,1)-difference set mentioned above.