Glasnik Matematicki, Vol. 50, No. 1 (2015), 1-15.

PRIMITIVE BLOCK DESIGNS WITH AUTOMORPHISM GROUP PSL(2,Q)

Snježana Braić, Joško Mandić and Tanja Vučičić

Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia
e-mail: sbraic@pmfst.hr

Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia
e-mail: majo@pmfst.hr

Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia
e-mail: vucicic@pmfst.hr

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.

2010 Mathematics Subject Classification.   05B05.

Key words and phrases.   Block design, automorphism group, primitive action.

Full text (PDF) (free access)

DOI: 10.3336/gm.50.1.01

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