Complete Classification of Flag-Transitive Point一Primitive " g8 A+ _8 M2 I7 M. `3 h9 D- } 2-Designs with Socle; \8 c2 ?6 i% |% t& C
. y( q- m" W; k$ z6 z( G In recent years several authors have determined some 2-designs with flag-transitive point-primitive automorphism group G of almost simple type with sporadic socle. Here we obtain the complete classification of flag-transitive point-primitive non-trivial 2-designs with socle Mli,and find that there are precisely 14 such nonisomorphic 2-designs. / b* A6 ~: W% F! u1 d1 A3 b4 D e9 d/ y9 K q$ O( R) r% q Keywords 2-design; flag-transitive; point-primitive; Mathieu group # ?! ^! z$ z, y% u( S9 f ! j0 S/ S# I! H9 M$ S" v- j