par Buekenhout, Francis 
;Doyen, Jean ;Delandtsheer, Anne
Référence Journal of combinatorial theory. Series A, 49, 2, page (268-293)
Publication Publié, 1988
;Doyen, Jean ;Delandtsheer, Anne Référence Journal of combinatorial theory. Series A, 49, 2, page (268-293)
Publication Publié, 1988
Article révisé par les pairs
| Résumé : | This paper is devoted to the study of finite linear spaces with a flag-transitive automorphism group. We survey known facts and introduce new results whose aim is to prepare a classification of such spaces and groups. In Section 1, we discuss various transitivity properties in finite linear spaces, and the relations between these properties. In Section 2, we give a list of examples of flag-transitive finite linear spaces, and the corresponding groups. In Section 3, we present some useful consequences of flag-transitivity. In Sections 4 and 5, we use the O'Nan-Scott theorem on primitive permutation groups to prove our main result: any group acting flag-transitively on a finite linear space is either of affine type or of simple type. In Section 6, we prove as a corollary that, with only one exception, any group acting transitively on the lines of a finite affine space must contain the translation group. © 1988. |
