AN ONANSCOTT THEOREM FOR FINITE QUASIPRIMITIVE PERMUTATION-GROUPS ANDAN APPLICATION TO 2-ARC TRANSITIVE GRAPHS

A permutation group is said to be quasiprimitive if each of its nontri vial normal subgroups is transitive. A structure theorem for finite qu asiprimitive permutation groups is proved, along the lines of the O'Na n-Scott Theorem for finite primitive permutation groups. It is shown t hat every finite, non-bipartite, 2-arc transitive graph is a cover of a quasiprimitive 2-arc transitive graph. The structure theorem for qua siprimitive groups is used to investigate the structure of quasiprimit ive 2-arc transitive graphs, and a new construction is given for a fam ily of such graphs.