On Designs from the Character Tables of Finite Groups

Document Type : Original Article

Authors

Clarence Mokalapa ¹

Amin Saeidi ²

Thekiso Seretlo ³

¹ Department of Mathematics and Applied Mathematics, Faculty of Science and Agriculture, Polokwane, University of Limpopo, South Africa

² Department of Mathematics and Applied Mathematics, University of Limpopo, Polokwane, South Africa

³ Department of Mathematics and Statistical Sciences, North-West University, Mafikeng, South Africa

10.22034/kjm.2025.511987.3483

Abstract

The aim of this paper is to construct certain designs using the maximal subgroups and conjugacy classes of finite primitive groups with known character tables. Our method is based on a result of Key and Moori, commonly referred to in the literature as the second Key-Moori method. We analyze the character table to identify permutation characters corresponding to the group’s primitive actions. Our focus is on the symplectic group PSp_{4}(q), where q is a prime power. However, the approach is general and can be applied to any primitive group.

Keywords

Projective symplectic group

Key-Moori methods

permutation character

design

Subjects

• 05 Combinatorics

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