Glasnik Matematicki, Vol. 42, No.2 (2007), 257-272.

A SERIES OF FINITE GROUPS AND RELATED SYMMETIC DESIGNS

Dieter Held, Mario-Osvin Pavčević and Marcel Schmidt

Department of applied mathematics, Faculty of electrical engineering, University of Zagreb, Unska 3, HR-10000 Zagreb, Croatia
e-mail: mario.pavcevic@fer.hr

Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, Theodor-Lieser-Strasse 5, D-06120 Halle (Saale), Germany
e-mail: mail@marcel-schmidt.net

Abstract.   For any odd prime power q = p^e we study a certain solvable group G of order q² · ((q-1)/2)² · 2 and construct from its internal structure a symmetric design D with parameters (2q²+1, q², (q²-1)/2) on which G acts as an automorphism group. As a consequence we find that the full automorphism group of D contains a subgroup of order |G| · e².

2000 Mathematics Subject Classification.   05E20, 05B05.

Key words and phrases.   Symmetric design, automorphism group.

DOI: 10.3336/gm.42.2.01

References:

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3. D. Held and M.-O. Pavcevic, A Series of Hadamard Designs with Large Automorphism Groups, J. Algebra 234 (2000), 620-626.
   MathSciNet     CrossRef

4. E. Lander, Symmetric Designs: An Algebraic Approach, Cambridge University Press, 1983.
   MathSciNet