Flag-transitive 2-(v, k, λ) Designs with (v − 1, k − 1) = 2 and Almost Simple Groups of Suzuki Type

Abstract

Suppose that

\mathcal{D}

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\cal{D}$$\end{document}

is a 2-(v, k, λ) design with (v − 1, k − 1) = 2 and that G is a flag-transitive group of automorphisms of

\mathcal{D}

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\cal{D}$$\end{document}

. It is shown in this paper that either G is 2-transitive on points or G is a subgroup of the group AΓL(1, v) of 1-dimensional semilinear affine transformations, so that

\mathcal{D}

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\cal{D}$$\end{document}

has v = p^d points (p is a prime). Further, we classify such type of designs admitting an almost simple automorphism group G with socle a Suzuki group Sz(q), by considering the classification under the (even weaker) assumption that k is odd. As its application, we construct two new families of flag-transitive 2-designs with socle Sz(q).

Keywords

2-design / automorphism group / flag-transitive / Suzuki group / 05B05 / 05B25 / 05E18 / 20B25

References

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