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A Construction of Designs from PSL(2,q) and PGL(2,q), q=1 mod 6, on q+2 Points

In: Algorithmic Algebraic Combinatorics and Gröbner Bases

Author

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  • Izumi Miyamoto

    (University of Yamanashi, Department of Computer Science and Media Engineering)

Abstract

Summary Let G=PSL(2,q) or PGL(2,q). We consider the action of G on the projective line together with one additional point, which is fixed by G. Assume q≡1 mod 6 and set $$ \lambda {}_q = \frac{1}{{24}}\left( {q - 1} \right)\left( {q - 3} \right)\left( {q - 5} \right). $$ We construct $$ 3 - \left( {q + 2,\frac{1}{2}\left( {q - 1} \right),{\lambda _q}} \right) $$ designs admitting PSL(2,q) as their automorphisms, if q≡3 mod 4. We also construct $$ 3 - \left( {q + 2,\frac{1}{2}\left( {q - 1} \right),2{\lambda _q}} \right) $$ designs admitting PGL(2,q) as their automorphisms. These designs may not be simple.

Suggested Citation

  • Izumi Miyamoto, 2009. "A Construction of Designs from PSL(2,q) and PGL(2,q), q=1 mod 6, on q+2 Points," Springer Books, in: Mikhail Klin & Gareth A. Jones & Aleksandar Jurišić & Mikhail Muzychuk & Ilia Ponomarenko (ed.), Algorithmic Algebraic Combinatorics and Gröbner Bases, pages 279-284, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-01960-9_10
    DOI: 10.1007/978-3-642-01960-9_10
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