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A classification of linear spaces based on quadrangles III

par Buekenhout, Francis ;Totten, Jim
Référence Geometriae dedicata, 8, 4, page (423-435)
Publication Publié, 1979-12

Article révisé par les pairs

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Résumé :

A quadrangle in a linear space can have at most 3 diagonal points. Denoting by d(Q) the number of diagonal points of a quadrangle Q, we say that a linear space L is of type T ⊂ {0, 1, 2, 3}, if T is the set of values taken by d(Q) for all quadrangles Q in L. This determines a classification of linear spaces into 16 possible types. In this paper we discuss type {0, 2} finite linear spaces, determining precisely the nature of their planes and establishing a strong relationship between them and the group theoretic work of Fischer and Aschbacher and Hall. © 1979 D. Reidel Publishing Co.