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Symmetric $1$-designs from $PSL_{2}(q),$ for $q$ a power of an odd prime | ||
| Transactions on Combinatorics | ||
| دوره 10، شماره 1، خرداد 2021، صفحه 43-61 اصل مقاله (300.16 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2020.123692.1740 | ||
| نویسندگان | ||
| Xavier Mbaale1؛ Bernardo G. Rodrigues* 2 | ||
| 1School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000 South Africa | ||
| 2Department of Mathematics and Applied Mathematics University of Pretoria Hatfield 0028 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| 1-design؛ symmetric designs؛ primitive design؛ projective special linear group | ||
| مراجع | ||
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