Geometry of Defining Relations in Groups

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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.