The first multiplier theorem supplies numerical multipliers for planar difference sets in Abelian groups. Let 
be a planar difference set of difference
set order 
in a finite Abelian group 
, and let 
be a positive divisor
of 
. Then 
is a numerical multiplier of 
(Gordon 1994, p. 2).
A multiplier is a group automorphism 
of 
which takes 
to a translation 
of itself for some 
.
If 
is of the form 
for an integer 
relatively prime to the group
order of 
, then 
is called a numerical multiplier.
."
Elec. J. Combin. 1, R6, 1994.