Glasnik Matematicki, Vol. 40, No.1 (2005), 1-11.

BIPLANES (56,11,2) WITH A FIXED-POINT-FREE INVOLUTORY AUTOMORPHISM

Mario Essert and Ljubo Marangunic

Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, I. Lucica 1, 10000 Zagreb, Croatia
e-mail: messert@fsb.hr

Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia
e-mail: ljubo.marangunic@fer.hr

Abstract.   The aim of this article is to prove that exactly four biplanes with parameters (56,11,2) admit a fixed-point-free action of an involutory automorphism. These are: Hall's biplane B20, Salwach and Mezzaroba's biplane B22, Denniston's biplane B24 and Denniston's biplane B26.

2000 Mathematics Subject Classification.   05B05.

Key words and phrases.   Biplane, design, automorphism group, orbit, orbit structure.

Full text (PDF) (free access)

DOI: 10.3336/gm.40.1.01

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