Geometry of Defining Relations in Groups

Inhaltsverzeichnis

• 1 General concepts of group theory.
• §1 Definition and examples of groups.
• §2 Cyclic groups and subgroups. Generators.
• §3 Cosets. Factor groups. Homomorphisms.
• §4 Relations in groups and free groups.
• 2 Main types of groups and subgroups.
• §5 p-subgroups in finite and abelian groups.
• §6 Soluble groups. Laws.
• §7 Finiteness conditions in groups.
• 3 Elements of two-dimensional topology.
• §8 Toplogical spaces.
• §9 Surfaces and their cell decomposition.
• §10 Topological invariants of surfaces.
• 4 Diagrams over groups.
• §11 Visual interpretation of the deduction of consequences of defining relations.
• §12 Small cancellation theory.
• §13 Graded diagrams.
• 5 A-maps.
• §14 Contiguity submaps.
• §15 Conditions on the grading.
• §16 Exterior arcs and ?-cells.
• §17 Paths that are nearly geodesic and cuts on A-maps.
• 6 Relations in periodic groups.
• §18 Free Burnside groups of large odd exponent.
• §19 Diagrams as A-maps. Properties of B(A, n).
• 7 Maps with partitioned boundaries of cells.
• §20 Estimating graphs for B-maps.
• §21 Contiguity and weights in B-maps.
• §22 Existence of ?-cells and its consequences.
• §23 C-maps.
• §24 Other conditions on the partition of the boundary of a map.
• 8 Partitions of relators.
• §25 General approach to presenting the groups G(i) and properties of these groups.
• §26 Inductive step to G(i+ 1). The group G(?).
• 9 Construction of groups with prescribed properties.
• §27 Constructing groups with subgroups of bounded order.
• §28 Groups with all subgroups cyclic.
• §29 Group laws other than powers.
• §30 Varieties in which all finite groups are abelian.
• 10 Extensions of aspherical groups.
• §31 Central extensions.
• §32 Abelian extensions and dependence among relations.
• 11 Presentations in free products.
• §33Cancellation diagrams over free products.
• §34 Presentations with condition R.
• §35 Embedding theorems for groups.
• §36 Operations on groups.
• 12 Applications to other problems.
• §37 Growth functions of groups and their presentations.
• §38 On group rings of Noetherian groups.
• §39 Further applications of the method.
• 13 Conjugacy relations.
• §40 Conjugacy cells.
• §41 Finitely generated divisible groups.
• Some notation.
• Author Index.