Some designs from the fixed points of alternating groups

Kekana, Madimetja Jan; Saeidi, Amin; Seretlo, Thekiso

doi:10.22108/toc.2025.141435.2178

Some designs from the fixed points of alternating groups

Articles in Press

Document Type : Research Paper

Authors

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

² Department of mathematics and Applied Mathematics, University of Limpopo, South Africa.

³ Department of Pure and Applied Analytics, North West University, mafikeng Campus, Mmabatho, South Africa.

10.22108/toc.2025.141435.2178

Abstract

In this paper, we construct some $1-(v,k,\lambda)$ designs from the alternating group $G=A_{n}$ with the maximal subgroup isomorphic to $M=A_{n-1}$. The method we use is called Key-Moori Method $2$. Furthermore, from the set $I_x$ which is the intersection of all blocks containing the point $x\in G$, we construct corresponding reduced designs. Our aim is to give explicit formulae to compute the parameters of the designs based on the cyclic structures of the permutations in $G$.

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