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Advances in Geometry
Translation planes of order q t and kernel containing K G GFðqÞ admitting fixedpoint-free collineation groups GK Ã , each of whose point orbits is the set of nonzero vectors of a 2-dimensional K-subspace, are shown to permit spread-retraction and produce either Baer subgeometry or mixed partitions of a corresponding projective space. When the same translation plane or spread produces a number of partitions of isomorphic projective spaces, we call this multiple spread-retraction. This analysisdoi:10.1515/advg.2003.016 fatcat:zshxmaztzzcurjr3ef3vv37fre