On representing finite lattices as intervals in subgroup lattices of finite groups

Let M-n be the lattice of length 2 with n greater than or equal to 1 atoms. It is an open problem to decide whether or not every such lattice (or indeed whether or not every finite lattice) can be represented as an interval in the subgroup lattice of some finite group. We complete the work of the second author, Lucchini, by reducing this problem to a series of questions concerning the finite non-abelian simple groups. (C) 1997 Academic Press.