ENGLISH

Topics in combinatorial group theory

By Gilbert Baumslag

Book information

Publisher
Birkhäuser
Year
1993
ISBN
9780817629212, 9783764329211, 0817629211, 3764329211
LCC
QA182.5 .B38 1993
Open Library ID
OL1401116M
Language
english
Format
PDF
Filesize
2 MB (2078470 bytes)
Series
Lectures in mathematics ETH Zurich
Edition
1
Pages
203\203
Library
Kolxo3
Scanned
yes
Time added
2009-07-20 03:45:11

Description

Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about groups, typically of the following kind: Are the groups in a given class finite (e.g., the Burnside problem)? Finitely generated? Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.

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