A. Yu. Ol'shanskii

Geometry of Defining Relations in Groups (eBook, PDF)

• Format: PDF

Produktbeschreibung

Zur Zeit liegt uns keine Inhaltsangabe vor.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 505
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9789401136181
• Artikelnr.: 43985528

Inhaltsangabe

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.