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Transitive $t$-designs and strongly regular graphs constructed from linear groups $L(2,q)$, $q \leq 23$ | ||
| International Journal of Group Theory | ||
| مقاله 5، دوره 8، شماره 3، آذر 2019، صفحه 43-64 اصل مقاله (256.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2017.21613 | ||
| نویسندگان | ||
| Dean Crnković؛ Andrea Švob* | ||
| Department of Mathematics, University of Rijeka, Rijeka, Croatia | ||
| چکیده | ||
| In this paper we construct transitive $t$-designs from the linear groups $L(2,q), q \leq 23$. Thereby we classify $t$-designs, $t \ge 2$, admitting a transitive action of the linear groups $L(2,q), q \leq 23$, up to 35 points and obtained numerous transitive designs, for $36\leq v\leq 55$. In many cases we proved the existence of $t$-designs with certain parameter sets. Among others we constructed $t$-designs with parameters $2$-$(55,10,4)$, $3$-$(24,11,495)$, $3$-$(24,12, 5m), m \in \{11, 12,22, 33, 44, 66, 132\}$. Furthermore, we constructed strongly regular graphs admitting a transitive action of the linear groups $L(2,q), q \leq 23$. | ||
| کلیدواژهها | ||
| $t$-design؛ strongly regular graph؛ linear group؛ Transitive group | ||
| مراجع | ||
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