Atnaujinkite slapukų nuostatas

Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations 2nd edition [Minkštas viršelis]

4.11/5 (14 ratings by Goodreads)
, ,
  • Formatas: Paperback / softback, 464 pages, aukštis x plotis x storis: 214x136x22 mm, weight: 471 g, Illustrations, unspecified
  • Serija: Dover Books on Mathema 1.4tics
  • Išleidimo metai: 25-Feb-2005
  • Leidėjas: Dover Publications Inc.
  • ISBN-10: 0486438309
  • ISBN-13: 9780486438306
Kitos knygos pagal šią temą:
Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations 2nd editionDidesnis paveikslėlis
  • Formatas: Paperback / softback, 464 pages, aukštis x plotis x storis: 214x136x22 mm, weight: 471 g, Illustrations, unspecified
  • Serija: Dover Books on Mathema 1.4tics
  • Išleidimo metai: 25-Feb-2005
  • Leidėjas: Dover Publications Inc.
  • ISBN-10: 0486438309
  • ISBN-13: 9780486438306
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780486438306.html
Raktažodžiai:
This classic graduate text builds from the basics of combinational group theory in the construction of groups from generators and defining relators, to Dehn's fundamental problem, definition and elementary properties of free groups, and Tietze transformations. It then describes factor groups and subgroups (the Reidemeister-Schreier method), Nielsen transformations, free products and free products with amalgamations, commutator calculus, and some recent developments in the field. The authors supply lists of theorems, corollaries definitions, symbols and abbreviations. This is a reprint of the 1976 edition originally published by Interscience Publishers. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

This seminal, much-cited account begins with a fairly elementary exposition of basic concepts and a discussion of factor groups and subgroups. The topics of Nielsen transformations, free and amalgamated products, and commutator calculus receive detailed treatment. The concluding chapter surveys word, conjugacy, and related problems; adjunction and embedding problems; and more. Second, revised 1976 edition.
Technical Remarks
Chapter 1 Basic Concepts
1.1 Introduction
1(11)
1.2 Construction of groups from generators and defining relators
12(12)
1.3 Dehn's fundamental problems
24(9)
1.4 Definition and elementary properties of free groups
33(15)
1.5 Tietze transformations
48(8)
1.6 Graph of a group
56(15)
Chapter 2 Factor Groups and Subgroups
2.1 Factor groups
71(3)
2.2 Verbal subgroups and reduced free groups
74(12)
2.3 Presentations of subgroups (The Reidemeister-Schreier method)
86(18)
2.4 Subgroups of free groups
104(16)
Chapter 3 Nielsen Transformations
3.1 Introduction
120(1)
3.2 A reduction process
121(19)
3.3 The commutator quotient group
140(13)
3.4 A test for isomorphism
153(9)
3.5 The automorphism group Φn of free groups
162(7)
3.6 Free automorphisms and free isomorphisms
169(3)
3.7 Braid groups and mapping class groups
172(8)
Chapter 4 Free Products and Free Products with Amalgamations
4.1 Free products
180(17)
4.2 Free product with amalgamated subgroups
197(30)
4.3 Subgroup theorems for free and amalgamated products
227(25)
4.4 Groups with one defining relator
252(35)
Chapter 5 Commutator Calculus
5.1 Introduction
287(1)
5.2 Commutator identities
288(4)
5.3 The lower central series
292(6)
5.4 Some freely generated graded algebras
298(10)
5.5 A mapping of a free group into Α(Ζ, r)
308(9)
5.6 Lie elements and basis theorems
317(19)
5.7 The lower central series of free groups
336(13)
5.8 Some applications
349(8)
5.9 Identities
357(11)
5.10 The Baker-Hausdorff formula
368(5)
5.11 Power relations and commutator relations
373(6)
5.12 Burnside's problem, Exponents 3 and 4
379(7)
5.13 Burnside's problem, Report on e > 4
386(2)
5.14 Topological aspects
388(5)
5.15 Free differential calculus
393(3)
Chapter 6 Introduction to Some Recent Developments
6.1 Word, conjugacy, and related problems
396(5)
6.2 Adjunction and embedding problems
401(5)
6.3 Varieties of groups
406(4)
6.4 Products of groups
410(3)
6.5 Residual and Hopfian properties
413(8)
References 421(15)
List of Theorems, Corollaries, and Definitions 436(2)
List of Symbols and Abbreviations 438(3)
Index 441