$2$-transitive symmetric designs

Classification of 2-transitive symmetric designs

All symmetric designs are determined for which the automorphism group is 2-transitive on the set of points. This note contains a proof of the following result. Theorem. Let D be a symmetric design with v > 2k such that Aut D is 2-transitive on points. Then D is one o f the following: (i) a projective space; (ii) the unique Hadamard design with v = I 1 and k = 5; (iii) a unique design with v = 1...

Imprimitive flag-transitive symmetric designs

A recent paper of O’Reilly Regueiro obtained an explicit upper bound on the number of points of a flagtransitive, point-imprimitive, symmetric design in terms of the number of blocks containing two points. We improve that upper bound and give a complete list of feasible parameter sequences for such designs for which two points lie in at most ten blocks. Classifications are available for some of...

ibn 2 - TRANSITIVE DESIGNS

2-Transitive and ag-transitive designs

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 ...

2 - Transitive and flag - transitive designs

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 ma...