Abstract
Let Γ be a [L.Af*]-geometry, that is a rank 3 geometry with linear spaces as plane residues, with dual affine planes as point residues and with generalized digons as line residues. Assume that (LL) holds in Γ. In the particular case where the plane residues are finite circles, the structure of such geometries has been strongly restricted by A. P. Sprague. Moreover, C. Lefevre and L. Van Nypelseer have given a complete classification of such geometries under the assumption that the plane residues are affine planes. We generalize these two results for [L.Af*]-geometries.
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