Block transitive 2−(v,k,1) designs and PGL2(q) groups

摘要

The article mainly deal with the block-transitive automorphism groups of 2−(v,k,1) designs. Let G=PGL2(q) for q a power of an odd prime number. We prove that if G acts block-transitively on a non-trivial 2−(v,k,1) design D then D is either a projective plane or 2−(136,10,1) design.