Geometry of Defining Relations in Groups [electronic resource] /

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 -- §33 Cancellation 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.

Bibliographic Details

Main Authors:	Ol’shanskii, A. Yu. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Dordrecht : Springer Netherlands : Imprint: Springer, 1991
Subjects:	Mathematics., Computer science, Group theory., Geometry., Manifolds (Mathematics)., Complex manifolds., Group Theory and Generalizations., Discrete Mathematics in Computer Science., Manifolds and Cell Complexes (incl. Diff.Topology).,
Online Access:	http://dx.doi.org/10.1007/978-94-011-3618-1
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