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Let S = (P,B, I) be a finite generalized quadrangle (GQ) having order (s, t). Let p be a point of S. A whorl about p is a collineation of S fixing all the lines through p. An elation about p is a whorl that does not fix any point not collinear with p, or is the identity. If S has an elation group acting regularly on the set of points not collinear with p we say that S is an elation generalized quadrangle (EGQ) with base point p. The following question has been posed: Can there be two non-isomorphic elation groups about the same point p? In this presentation, we show that there are exactly two (up to isomorphism) elation groups of the Hermitian surface H(3, q) over a finite field of characteristic 2.

Elation groups of the Hermitian surface H(3,q2) over a finite field of characteristic 2