۱-Designs Constructed from the Groups PSL_{۲}(۸۱) and PSL_{۲}(۸۹)

In this paper, some designs from the primitive permutation representations of the groups PSL_۲(۸۱) and PSL_۲(۸۹) are constructed using the Key-Moori Method ۱. We determine the automorphism groups of all the obtained designs and prove that the groups PSL_۲(۸۱), PSL_۲(۸۱){}^{.}۲, PSL_۲(۸۱)\text{:}۲, PGL_۲(۸۱), P\Sigma L_۲(۸۱), P\Gamma L_۲(۸۱), PSL_۲(۸۹) and PSL_۲(۸۹)\text{:}۲ appear as the automorphism groups of these constructed designs.

کلیدواژه ها:

design ، group action ، automorphism group ، projective special linear group