Flag-transitive 2-designs with prime square replication number and alternating groups.

This paper contributes to the classification of flag-transitive 2-designs. Let D be a 2- (v , k , λ) design with prime square replication number. Suppose that G is a flag-transitive, point-primitive automorphism group of D with socle an alternating group. We prove that D is the unique 2-(10, 6, 5) design with G = A l t (6) or Sym(6). [ABSTRACT FROM AUTHOR]