An identity for subgroup lattices of Abelian groups
This well-written, important paper contains the solution of the following long-standing problem: Does there exist a lattice-identity holding in the subgroup lattice of every Abelian group which fails in the lattice of normal subgroups of some finite group? The Theorem of this paper presents such an identity. It fails for a two- group. The paper mentions an unpublished result of Emil Kiss and the first author ``on the road'' leading to this theorem. The authors give only a rough sketch on the projective geometric background of the theorem. Those who want to understand the geometric part should read the longer version: ``Congruence varieties of groups and Abelian groups'', written by the same authors, which will appear in: Lattice Theory and its Application (edited by K. A. Baker and R. Wille), 163-183 (Heldermann Verlag, 1995).
scientific article; zbMATH DE number 750788