First Multiplier Theorem

Let $D$ be a planar Abelian Difference Set and $t$ be any Divisor of $n$. Then $t$ is a numerical multiplier of $D$, where a multiplier is defined as an automorphism $\alpha$ of $G$ which takes $D$ to a translation $g+D$ of itself for some $g\in G$. If $\alpha$ is of the form $\alpha:x\to tx$ for $t\in\Bbb{Z}$ relatively prime to the order of $G$, then $\alpha$ is called a numerical multiplier.

References

Gordon, D. M. ``The Prime Power Conjecture is True for $n<2,000,000$.'' Electronic J. Combinatorics 1, R6 1-7, 1994. http://www.combinatorics.org/Volume_1/volume1.html#R6.