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Title
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The Residually Weakly Primitive Geometries of Sym(5)x2
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Authors
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Philippe Cara and Dimitri Leemans
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Reference
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Discrete Math. 255(2002), nr. 1-3, 35-45.
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Math. Reviews
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2003i: 51012.
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Abstract
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We classify all firm and residually connected geometries satisfying the
intersection property (IP)_2, and on which the group Sym(5)x2 acts
flag-transitively and residually weakly primitively. This work was motivated
by a study of the Ivanov-Shpectorov geometry for the O'Nan sporadic simple
group. We show that all geometries are either direct sums
of geometries of Sym(5) and 2 satisfying the same properties or are
extensions of lower rank geometries given by a theorem of
Leemans (see Leemans' Master's Thesis).
The results obtained here rely partially on computer algebra.
The list of geometries of Sym(5)x2 can be downloaded in Postscript version.
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