, which are subsets of 
, there correspond
certain subgroups of 
. For each 
we introduce its
stabilizer :
This is the subgroup of elements of that stabilize the point 
There is
also the subgroup of elements which pointwise stabilize the elements of
a subset 
of 
and which is called the pointwise stabilizer
of 
in contrast to the setwise stabilizer
of 
We note in passing that 
that 
and that this notation is compatible
with the notation 
for the kernel of the permutation representation
corresponding to 