Author | Suzuki, Michio. author |
---|---|
Title | Structure of a Group and the Structure of its Lattice of Subgroups [electronic resource] / by Michio Suzuki |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1956 |
Connect to | http://dx.doi.org/10.1007/978-3-642-52758-6 |
Descript | VIII, 96 p. 1 illus. online resource |
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