Bounds on finite quasiprimitive permutation groups

A permutation group is said to be quasiprimitive if every nontrivial normal subgroup is transitive. Every primitive permutation group is quasiprimitiv e, but the converse is not true. In this paper we start a project whose goa l is to check which of the classical results on finite primitive permutatio n groups also holds for quasiprimitive ones (possibly with some modificatio ns). The main topics addressed here are bounds on order, minimum degree and base size, as well as groups containing special p-elements. We also pose s ome problems for further research.