On some designs constructed from the groups $PSL_{2}(q)$, $q=53,61,64$

Document Type : Research Paper


Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran



In this paper, we use the primitive permutation representations of the simple groups $PSL_2(53)$, $PSL_2(61)$ and $PSL_2(64)$ and construct 1-designs by the Key-Moori Method 1.
It is shown that the groups $PSL_2(53)$, $PSL_2(53)\text{:}2$, $PSL_2(61)$, $PSL_2(61)\text{:}2$, $PSL_2(64)$, $PSL_2(64)\text{:}2$, $PSL_2(64)\text{:}3$ and $PSL_2(64)\text{:}6$ appear as the full automorphism groups of these obtained designs.


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