Reza Kahkeshani - 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_۲(۵۳), PSL_۲(۶۱) and PSL_۲(۶۴) and construct ۱-designs by the Key-Moori Method ۱.It is shown that the groups PSL_۲(۵۳), PSL_۲(۵۳)\text{:}۲, PSL_۲(۶۱), PSL_۲(۶۱)\text{:}۲, PSL_۲(۶۴), PSL_۲(۶۴)\text{:}۲, PSL_۲(۶۴)\text{:}۳ and PSL_۲(۶۴)\text{:}۶ appear as the full automorphism groups of these obtained designs.

Design, Automorphism group, Projective special linear group