Vol. 5, No. 1, 2007

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

Robert L. Rostermundt

Vol. 5 (2007), No. 1, 117–128

Let S = (P,,) be a finite generalized quadrangle having order (s,t). Let p be a point of S. A whorl about p is a collineation of § 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 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,q2) over a finite field of characteristic 2.

generalized quadrangles, elation groups, Hermitian surface
Mathematical Subject Classification 2000
Primary: 51E12
Received: 5 April 2007
Accepted: 22 April 2007
Robert L. Rostermundt