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

The central theme of this monograph is the relation between the structure of a group and the structure of its lattice of subgroups. Since the first papers on this topic have appeared, notably those of BAER and ORE, a large body of literature has grown up around this theory, and it is our aim to give...

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Bibliographic Details
Main Author: Suzuki, Michio
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1956, 1956
Edition:1st ed. 1956
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
Subjects:
Group Theory And Generalizations
Group Theory
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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

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