Symmetric $1$-designs from $PSL_{2}(q),$ for $q$ a power of an odd prime

Document Type: Research Paper

Authors

1 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000 South Africa

2 Department of Mathematics and Applied Mathematics University of Pretoria Hatfield 0028

10.22108/toc.2020.123692.1740

Abstract

Let $G = \PSL_{2}(q)$‎, ‎where $q$ is a power of an odd prime‎. ‎Let $M$ be a maximal subgroup of $G$‎. ‎Define $\left\lbrace \frac{|M|}{|M \cap M^g|}‎: ‎g \in G \right\rbrace$ to be the set of orbit lengths of the primitive action of $G$ on the conjugates of a maximal subgroup $M$ of $G.$ By using a method described by Key and Moori in the literature‎, ‎we construct all primitive symmetric $1$-designs that admit $G$ as a permutation group of automorphisms‎.

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