Let
be a finite generalized
quadrangle having order ().
Let
be a point of
. A
whorl about
is a collineation
of
fixing all the
lines through
. An
elation about
is a whorl that does not fix any point not collinear with
, or is the
identity. If
has an elation group acting regularly on the set of points not collinear with
we say
that
is an elation generalized quadrangle with base point
. The following
question has been posed: Can there be two non-isomorphic elation groups about the same
point
? In this
presentation, we show that there are exactly two (up to isomorphism) elation groups of the
Hermitian surface
over a finite field of characteristic 2.