|
|
|||
|
||||
OverviewThe main feature of this book is a systematic application of elementary geometric and topological techniques for solving problems that arise naturally in algebra. After an account of preliminary material, there is a discussion of a geometrically intuitive interpretation of the derivation of consequences of defining relations of groups. A study is made of planar and certain other two-dimensional maps connected with well-known problems in general group theory, such as the problems of Burnside and O. Yu. Schmidt. The method of cancellation diagrams developed here is applied to these and to a series of other problems. This monograph is addressed to research workers and students in universities, and may be used as a basis for a series of specialized lectures or seminars. Full Product DetailsAuthor: A.Yu. Ol'shanskii , Y. A. BakhturinPublisher: Springer Imprint: Springer Edition: 1991 ed. Volume: 70 Dimensions: Width: 15.50cm , Height: 3.10cm , Length: 23.50cm Weight: 0.963kg ISBN: 9780792313946ISBN 10: 0792313941 Pages: 505 Publication Date: 31 October 1991 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Out of stock The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of Contents1 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |