Abstract
In this paper we consider finite nets of orderq 2 and degreeq + 1 which admit GL(2,q). Our main result says that if a net\(\mathcal{N}\) of orderq 2 and degreeq + 1 admits a collineation group ℊ with a point-regular normal subgroupT such that ℊ/T ⋍ GL(2,q), then\(\mathcal{N}\) is isomorphic to a regulus net, a twisted regulus net, a Hering net, or\(\mathcal{N}_5\). Except in the last one, each of them corresponds to a surface in PG(3,q) obtained from a homogeneous polynomial in two variables.
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Hiramine, Y. On nets of orderq 2 and degreeq+1 admitting GL(2,q). Geom Dedicata 48, 139–189 (1993). https://doi.org/10.1007/BF01264066
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DOI: https://doi.org/10.1007/BF01264066