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GEOMETRY OF DEFINING RELATIONS IN GROUPS (MATHEMATICS AND By A.yu. Ol'shanskii - A. Y. Ol'shanskii
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A. Y. Ol'shanskii:

GEOMETRY OF DEFINING RELATIONS IN GROUPS (MATHEMATICS AND By A.yu. Ol'shanskii - hardcover

ISBN: 9780792313946

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Geometry of Defining Relations in Groups - A.Yu. Ol\\'shanski
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A.Yu. Ol\\'shanski:

Geometry of Defining Relations in Groups - hardcover

1991, ISBN: 0792313941

[EAN: 9780792313946], New book, [PU: Springer Netherlands], EDV THEORIE INFORMATIK MATHEMATIK GEOMETRIE RAUMLEHRE ABELIANGROUP GROUPTHEORY PARTITION ALGORITHMS SETS VERIFICATION ARITHMETI… More...

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Geometry of Defining Relations in Groups (Mathematics and its Applications, 70) - Ol'shanskii, A.Yu.
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Ol'shanskii, A.Yu.:
Geometry of Defining Relations in Groups (Mathematics and its Applications, 70) - hardcover

1991

ISBN: 9780792313946

Springer, Hardcover, Auflage: 1991, 531 Seiten, Publiziert: 1991-10-31T00:00:01Z, Produktgruppe: Book, 0.96 kg, Verkaufsrang: 11663052, Machine Theory, AI & Machine Learning, Computer Sci… More...

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Ol'Shanskii, A.Y.:
Geometry of Defining Relations in Groups - hardcover

1991, ISBN: 9780792313946

Hard cover, Mathematics|Mathematics, This is an ex-library book and may have the usual library/used-book markings inside. This book has hardback covers. Clean from markings. In good all r… More...

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Ol'shanskii A.Yu.:
Geometry of Defining Relations in Groups - hardcover

1991, ISBN: 0792313941

[EAN: 9780792313946], New book, [PU: Springer], Print on Demand pp. xxvi + 505, Books

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Details of the book
Geometry of Defining Relations in Groups (Mathematics and its Applications, 70)

The 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.

Details of the book - Geometry of Defining Relations in Groups (Mathematics and its Applications, 70)


EAN (ISBN-13): 9780792313946
ISBN (ISBN-10): 0792313941
Hardcover
Publishing year: 1991
Publisher: Springer

Book in our database since 2007-06-21T04:56:20-04:00 (New York)
Detail page last modified on 2023-06-09T16:51:57-04:00 (New York)
ISBN/EAN: 9780792313946

ISBN - alternate spelling:
0-7923-1394-1, 978-0-7923-1394-6
Alternate spelling and related search-keywords:
Book title: groups and geometry


Information from Publisher

Author: A.Yu. Ol'shanskii
Title: Mathematics and its Applications; Geometry of Defining Relations in Groups
Publisher: Springer; Springer Netherland
505 Pages
Publishing year: 1991-10-31
Dordrecht; NL
Language: English
128,39 € (DE)
131,99 € (AT)
142,00 CHF (CH)
Available
XXVI, 505 p.

BB; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Gruppen und Gruppentheorie; Verstehen; Abelian group; Group theory; Partition; algorithms; geometry; sets; verification; Group Theory and Generalizations; Discrete Mathematics in Computer Science; Manifolds and Cell Complexes; Geometry; Mathematik für Informatiker; Diskrete Mathematik; Topologie; Geometrie; BC

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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