BASES FOR PRIMITIVE PERMUTATION-GROUPS AND A CONJECTURE OF BABAI

A base of a permutation group G is a sequence B of points from the per mutation domain such that only the identity of G fixes B pointwise. We show that primitive permutation groups with no alternating compositio n factors of degree greater than d and no classical composition factor s of rank greater than d have a base of size bounded above by a functi on of d. This confirms a conjecture of Babai. (C) 1997 Academic Press.