Subgroup Lattices of Groups
1st Edition
Published on 20. July 2011
XV, 572 pages
978-3-11-086864-7 (ISBN)
Description
No detailed description available for "Subgroup Lattices of Groups".
Reviews / Votes
"In the opinion of the reviewer the book is very well written - to wait for a new book in this area almost 40 years has proved to be worthwhile." Zentralblatt für Mathematik
More details
Other editions
Additional editions
Roland Schmidt
Subgroup Lattices of Groups
Book
08/1994
1st Edition
De Gruyter
€220.00
Shipment within 7-9 days
Roland Schmidt
Subgroup Lattices of Groups
Book
01/1994
1st Edition
De Gruyter
€309.00
Article exhausted; check different version
Content
- Intro
- Preface
- Notation
- Chapter 1. Fundamental concepts
- 1.1 Basic concepts of lattice theory
- 1.2 Distributive lattices and cyclic groups
- 1.3 Projectivities
- 1.4 The group of autoprojectivities
- 1.5 Power automorphisms
- 1.6 Direct products
- Chapter 2. Modular lattices and abelian groups
- 2.1 Modular lattices
- 2.2 P-groups
- 2.3 Finite p-groups with modular subgroup lattices
- 2.4 Groups with modular subgroup lattices
- 2.5 Projectivities of M-groups
- 2.6 Projectivities between abelian groups
- Chapter 3. Complements and special elements in the subgroup lattice of a group
- 3.1 Groups with complemented subgroup lattices (K-groups)
- 3.2 Special complements
- 3.3 Relative complements
- 3.4 Neutral elements and related concepts
- 3.5 Finite groups with a partition
- Chapter 4. Projectivities and arithmetic structure of finite groups
- 4.1 Normal Hall subgroups
- 4.2 Singular projectivities
- 4.3 Op(G), Op(G), Fitting subgroup and hypercentre
- 4.4 Abelian p-subgroups and projectivities
- Chapter 5. Projectivities and normal structure of finite groups
- 5.1 Modular subgroups of finite groups
- 5.2 Permutable subgroups of finite groups
- 5.3 Lattice-theoretic characterizations of classes of finite groups
- 5.4 Projective images of normal subgroups of finite groups
- 5.5 Normal subgroups of p-groups with cyclic factor group
- 5.6 Normalizers, centralizers and conjugacy classes
- Chapter 6. Projectivities and normal structure of infinite groups
- 6.1 Subgroups of finite index
- 6.2 Permodular subgroups
- 6.3 Permutable subgroups of infinite groups
- 6.4 Lattice-theoretic characterizations of classes of infinite groups
- 6.5 Projective images of normal subgroups of infinite groups and index preserving projectivities
- 6.6 The structure of NG/NG and NG/NG and projective images of soluble groups
- Chapter 7. Classes of groups and their projectivities
- 7.1 Free groups
- 7.2 Torsion-free nilpotent groups
- 7.3 Mixed nilpotent groups
- 7.4 Periodic nilpotent groups
- 7.5 Soluble groups
- 7.6 Direct products of groups
- 7.7 Groups generated by involutions
- 7.8 Finite simple and lattice-simple groups
- Chapter 8. Dualities of subgroup lattices
- 8.1 Abelian groups with duals
- 8.2 The main theorem
- 8.3 Soluble groups with duals
- 8.4 Finite groups with duals
- 8.5 Locally finite groups with duals
- Chapter 9. Further lattices
- 9.1 Lattices of normal subgroups
- 9.2 Lattices of subnormal subgroups
- 9.3 Centralizer lattices
- 9.4 Coset lattices
- Bibliography
- Index of Names
- Index of Subjects
