engleski

Primitive Block Designs with Automorphism Group PSL(2, q)

We present the results of a research which aims to determine, up to isomorphism and complementation, all primitive block designs with the projective line F-q boolean OR {;infinity}; as the set of points and PSL (2, q) as an automorphism group. The obtained designs are classified by the type of a block stabilizer. The results are complete, except for the designs with block stabilizers in the fifth Aschbacher's class. In particular, the problem is solved if q is a prime. We include formulas for the number of such designs with q - p(2 alpha 3 beta), alpha, beta nonnegative integers.

Block design ; Automorphism group ; Primitive action

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