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

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

A chapter in Algorithmic Algebraic Combinatorics and Gröbner Bases, 2009, pp 279-284 from Springer

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.

Keywords: Block design; Superscheme; Permutation group; Homogeneous group (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01960-9_10

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DOI: 10.1007/978-3-642-01960-9_10

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