Groups : topological, combinatorial and arithmetic aspects

edited by T.W. Müller

In 1999 a number of eminent mathematicians were invited to Bielefeld to present lectures at a conference on topological, combinatorial and arithmetic aspects of (infinite) groups. The present volume consists of survey and research articles invited from participants in this conference. Topics covered include topological finiteness properties of groups, Kac-Moody groups, the theory of Euler characteristics, the connection between groups, formal languages and automata, the Magnus-Nielsen method for one-relator groups, atomic and just infinite groups, topology in permutation groups, probabilistic group theory, the theory of subgroup growth, hyperbolic lattices in dimension three, generalised triangle groups and reduction theory. All contributions are written in a relaxed and attractive style, accessible not only to specialists, but also to good graduate and post-graduate students, who will find inspiration for a number of basic research projects at various levels of technical difficulty.

「Nielsen BookData」より

[目次]

  • 1. Reductive groups as metric spaces H. Abels
  • 2. Finiteness properties of groups acting on twin buildings P. Abramenko
  • 3. Higher finiteness properties of S-arithmetic groups in the function field case I H. Behr
  • 4. Controlled topology and group actions R. Bieri and R. Geoghegan
  • 5. Finiteness properties of soluble S-arithmetic groups - a survey K. U. Bux
  • 6. Topology in permutation groups P. Cameron
  • 7. Euler characteristics of discrete groups I. Chiswell
  • 8. Intersection of Magnus subgroups of one-relator groups D. J. Collins
  • 9. A minimality property of certain branch groups R. I. Grigorchuk and J. S. Wilson
  • 10. Lattices with non-integral character H. Helling
  • 11. Some applications of probability in group theory A. Mann
  • 12. Parity patterns in Hecke groups and Fermat primes T. W. Muller
  • 13. Automorphisms of the binary tree: state-closed subgroups and dynamics of 1/2-endomorphisms V. Nekrashevych and S. Sidki
  • 14. The mapping class group of the twice punctured torus J. R. Parker and C. Series
  • 15. Kac-Moody groups: split and relative theories. Lattices B. Remy
  • 16. On the finite images of infinite groups D. Segal
  • 17. Pseudo-finite generalized triangle groups E. B. Vinberg and R. Kaplinsky.

「Nielsen BookData」より

この本の情報

書名 Groups : topological, combinatorial and arithmetic aspects
著作者等 Muller T.W. (Queen Mary University of London)
Müller T. W. (Thomas Wolfgang)
シリーズ名 London Mathematical Society lecture note series
出版元 Cambridge University Press
刊行年月 2004
ページ数 xvi, 587 p.
大きさ 23 cm
ISBN 0521542871
NCID BA66722542
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言語 英語
出版国 イギリス
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