2 - Transitive and flag - transitive designs
نویسنده
چکیده
Throughout this paper V always will denote a design with "t; points, k > 2 points per line, and>' = 1 line through any two different points. Let G <:: Aut (V). I will primarily be interested in the case in which G either is 2-transitive on the points of VOl' is transitive on the flags (incident point-line pairs) ofV. Note that 2-transitivity implies flag-transitivity since>. = 1. The subject matter has been separated partly along historical lines, but more significantly as regards the use of the classification of finite simple groups. §I involves comparatively little in the way of group-theoretic background (in p<U'ticul<U', it concerns results noticea,bly predating the aJorernen-tioned classification). §II describes the main results that use properties of simple groups. Finally, §III reverts to a more combinatorial and very much less group-theoretic problem: the construction of new flag-transitive designs. and [:3] for other surveys of similar material with somewhat d.ifferent ern-ph<:),ses. The most beautiful result concerning the type of question being considered here is the Ostrom-Wagner Theorem [,If I]: If V i8 a finile proiective plane
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تاریخ انتشار 1993