Original scientific paper

https://doi.org/10.3336/gm.50.1.01

Primitive block designs with automorphism group PSL(2,Q)

Snježana Braić ; Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia
Joško Mandić ; Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia
Tanja Vučičić orcid.org/0000-0003-1574-6297 ; Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia

Abstract

We present the results of a research which aims to determine, up to isomorphism and complementation, all primitive block designs with the projective line Fq∪{∞} 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=p2α3β, α,β nonnegative integers.

Keywords

Block design; automorphism group; primitive action

Hrčak ID:

140078

URI

https://hrcak.srce.hr/140078

Publication date:

15.6.2015.

Visits: 1.313 *