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.
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.
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