Intervals in the subgroup lattices of the alternating and symmetric groups of prime degree.

If G is a group and H is a subgroup of G we write for the lattice of over-groups of H in G. It is an open question whether or not every finite lattice is isomorphic to some finite group interval lattice , where G is finite. We prove that no DΔ( m1, ... , mt)-lattice and few M-lattices have the form , where G is an alternating or symmetric group of prime degree. [ABSTRACT FROM AUTHOR]