Structure of a Group and the Structure of its Lattice of Subgroups

I. Groups with a special kind of subgroup lattice.- 1. The distributive law in subgroup lattices.- 2. Modular identity in subgroup lattices.- 3. The Jordan-Dedekind chain condition and lower semi-modularity.- 4. Finite groups with a modular lattice of subgroups.- 5. Structure of infinite M-groups.- 6. Structure of UM-groups.- 7. Complemented groups.- II. Isomorphisms of subgroup lattices.- 1. Projectivities.- 2. Projectivities of abelian groups.- 3. Projectivities of locally free groups.- 4. Projectivities of finite groups.- 5. Projectivities of modular groups.- 6. Index-preserving Proj ectivities.- 7. The images of normal subgroups under projectivities of finite groups.- 8. The number of finite groups with given lattice of subgroups.- 9. The group of auto-proj ectivities.- 10. Projectivities of simple groups.- 11. Characteristic chains of subgroup lattices.- 12. Representation of lattices as subgroup lattices.- 13. The situation-preserving mappings.- III. Homomorphisms of subgroup lattices.- 1. The kernels of a homomorphism of a subgroup lattice.- 2. Complete L-homomorphisms onto cyclic groups.- 3. General properties of complete L-homomorphisms.- 4. L-homomorphisms induced by group-homomorphisms.- 5. Incomplete L-homomorphisms.- 6. L-homomorphisms of finite groups.- 7. The meet-homomorphisms.- 8. Structure of finite groups which admit a proper L-homomorphism.- 9. L-homomorphisms onto a nilpotent group.- IV. Dualisms of subgroup lattices.- 1. Dualisms (of abelian groups).- 2. Nilpotent groups with duals.- 3. Finite solvable groups with duals.