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 a toms. It is an open problem to decide whether or not every such lattic e (or indeed whether or not every finite lattice) can be represented a s an interval in the subgroup lattice of some finite group. We complet e 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.