Locally affine geometries of order 2 where shrinkings are affine expansions


Given a locally a affine geometry Γ of order 2 and a flag-transitive subgroup G ≤ Aut(Γ), suppose that the shrinkings of Γ are isomorphic to the a affine expansion of the upper residue of a line of Γ by a homogeneous representation in a 2-group. We shall prove that, under certain hypotheses on the stabilizers Gp and Gl of a point p and a line l, we have G=R{Gp} for a representation group R of Res(p). We also show how to apply this result in the classification of flag-transitive c-extended P- and T-geometries.

DOI Code: 10.1285/i15900932v24n2p97

Keywords: Shrinkings; Affine expansions; Representation groups; Sporadic groups

Classification: 51E24; 20D08; 20C34

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