\(\text{PSp}_4(3)\) as a symmetric (36, 15, 6)-design
type: Item
instance of: scholarly article
title: \(\text{PSp}_4(3)\) as a symmetric (36, 15, 6)-design
zbMATH Open document ID: 0935.05007
author: Dieter Held
author: Jörg Hrabě de Angelis
author: Mario-Osvin Pavčević
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1999-12-07T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108495
review text: Let \(G\) be a group isomorphic to \(\text{PSp}_4(3) \cong U_4(2)\) and let \(\mathcal P\) be the conjugacy class of subgroups of \(G\) isomorphic to \(S_6 \cong \text{Sp}_4(2)'\). Then \(S \in {\mathcal P}\) has three orbits \(\{S\}, B\) and \(C\) on \(\mathcal P\) of length \(1,15\) and \(20\), respectively. It is shown that \(({\mathcal P}, {\mathcal B}, I)\) is a symmetric \(2\)-\((36,15,6)\) design with set of blocks \({\mathcal B} = \{B^g \mid g \in G\}\) where a point \(R\) is incident with a block \(B^g\) if \(R\) is contained in \(B^g\). The automorphism group \(\Aut(G)\) acts on this design flag-transitively.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05E20
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 51E05
zbMATH DE Number: 1319596
zbMATH Keywords: symmetric design
zbMATH Keywords: symplectic group
reviewed by: Barbara Baumeister
MaRDI profile type: Publication
cites work: Q3684278
cites work: A Characterization of the Finite Simple Group PSp4(3)
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description: scientific article; zbMATH DE number 1319596