Subgroup Lattices of Groups

Name: Subgroup Lattices of Groups
Brand: De Gruyter
Price: 209.0 EUR
Availability: OnlineOnly

Roland Schmidt(Autor*in)

De Gruyter (Verlag)

1. Auflage

Erschienen am 20. Juli 2011

XV, 572 Seiten

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978-3-11-086864-7 (ISBN)

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Inhalt

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

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