Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Traces and Euler characteristics
- 2 Groups of virtually finite dimension
- 3 Free abelianised extensions of finite groups
- 4 Arithmetic groups
- 5 Topological methods in group theory
- 6 An example of a finite presented solvable group
- 7 SL3(Fq[t]) is not finitely presentable
- 8 Two-dimensional Poincaré duality groups and pairs
- 9 Metabelian quotients of finitely presented soluble groups are finitely presented
- 10 Soluble groups with coherent group rings
- 11 Cohomological aspects of 2-graphs. II
- 12 Recognizing free factors
- 13 Trees of homotopy types of ( m)-complexes
- 14 Geometric structure of surface mapping class groups
- 15 Cohomology theory of aspherical groups and of small cancellation groups
- 16 Finite groups of deficiency zero
- 17 Äquivalenzklassen von Gruppenbeschreibungen, Identitäten und einfacher Homotopietyp in niederen Dimensionen
- 18 Two-dimensional complexes with torsion values not realizable by self-equivalences
- 19 Applications of Nielsen's reduction method to the solution of combinatorial problems in group theory: a survey
- 20 Chevalley groups over polynomial rings
- List of problems
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Traces and Euler characteristics
- 2 Groups of virtually finite dimension
- 3 Free abelianised extensions of finite groups
- 4 Arithmetic groups
- 5 Topological methods in group theory
- 6 An example of a finite presented solvable group
- 7 SL3(Fq[t]) is not finitely presentable
- 8 Two-dimensional Poincaré duality groups and pairs
- 9 Metabelian quotients of finitely presented soluble groups are finitely presented
- 10 Soluble groups with coherent group rings
- 11 Cohomological aspects of 2-graphs. II
- 12 Recognizing free factors
- 13 Trees of homotopy types of ( m)-complexes
- 14 Geometric structure of surface mapping class groups
- 15 Cohomology theory of aspherical groups and of small cancellation groups
- 16 Finite groups of deficiency zero
- 17 Äquivalenzklassen von Gruppenbeschreibungen, Identitäten und einfacher Homotopietyp in niederen Dimensionen
- 18 Two-dimensional complexes with torsion values not realizable by self-equivalences
- 19 Applications of Nielsen's reduction method to the solution of combinatorial problems in group theory: a survey
- 20 Chevalley groups over polynomial rings
- List of problems
Summary
The reader may distinguish three principal themes in this volume. There is the direct development of homological methods, interlocking neatly with the Euler characteristic theory on one side, and finiteness questions on the other. There is the theory of groups acting on trees, including that of amalgamated free products and HNN groups, and also the Stallings structure theorem. Finally, but at present still in a rudimentary state, there is the technique of relation modules.
In contrast there is a need for examples, general enough to test ideas, but explicit enough to make detailed calculations. Much the most interesting at present are arithmetic and related groups; the study of these was an auxiliary theme.
Thanks are due to the LMS for backing the conference, to the SRC for money to run it, to David Johnson for much work on the organisation, to the staff at Grey College for providing an agreeable background and, of course, to the participants for their contributions.
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- Information
- Homological Group Theory , pp. vii - viiiPublisher: Cambridge University PressPrint publication year: 1979