2-Transitive and ag-transitive designs
نویسنده
چکیده
Throughout this paper D always will denote a design with v points, k > 2 points per line, and = 1 line through any two diierent points. Let G Aut (D). I will primarily be interested in the case in which G either is 2-transitive on the points of D or is transitive on the ags (incident point-line pairs) of D. Note that 2-transitivity implies ag-transitivity since = 1. The subject matter has been separated partly along historical lines, but more signiicantly as regards the use of the classiication of nite simple groups. xI involves comparatively little in the way of group-theoretic background (in particular, it concerns results noticeably predating the aforemen-tioned classiication). xII describes the main results that use properties of simple groups. Finally, xIII reverts to a more combinatorial and very much less group-theoretic problem: the construction of new ag-transitive designs. and 3] for other surveys of similar material with somewhat diierent emphases. The most beautiful result concerning the type of question being considered here is the Ostrom-Wagner Theorem 49]: If D is a nite projective plane
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