Symmetric $1$-designs from $PSL_{2}(q),$ for $q$ a power of an odd prime
نویسندگان
1 Department of Mathematics and Applied Mathematics University of Pretoria Hatfield 0028
2 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000 South Africa
doi
10.22108/toc.2020.123692.1740چکیده
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.
