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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.


Gordon, D. M. ``The Prime Power Conjecture is True for $n<2,000,000$.'' Electronic J. Combinatorics 1, R6 1-7, 1994.

© 1996-9 Eric W. Weisstein