On some designs constructed from the groups $PSL_2(q)$, $q=53,61,64$

چکیده مقاله

 In this paper, we use the primitive permutation representations of the simple groups PSL2(53)PSL2(53), PSL2(61)PSL2(61) and PSL2(64)PSL2(64) and construct 1-designs by the Key-Moori Method 1.
It is shown that the groups PSL2(53)PSL2(53), PSL2(53):2PSL2(53):2, PSL2(61)PSL2(61), PSL2(61):2PSL2(61):2, PSL2(64)PSL2(64), PSL2(64):2PSL2(64):2, PSL2(64):3PSL2(64):3 and PSL2(64):6PSL2(64):6 appear as the full automorphism groups of these obtained designs.