The Collineation Groups of Generalized Twisted Field Planes

We investigate autotopisms and isotopisms of generalized twisted field planes. A revision of Albert′s results is developed using a mixture of group-theoretical and algebraic methods. In particular, transitivity conditions of the autotopism group on the nonvertex points of one or more sides of the autotopism triangle are determined. Also, correlations and polarities in generalized twisted field planes are examined in detail. These results allow us to obtain several improvements of recent results in semifield planes.

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