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

Abstract

If G is a group and H is a subgroup of G we write O_G(H) 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 O_G(H), where G is finite. We prove that no DΔ(m1, … , mt)-lattice and few M-lattices have the form O_G(H), where G is an alternating or symmetric group of prime degree.

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