03306nam a22003138i 4500001001600000003000700016008004100023020001800064020001800082035002000100041000800120082001500128245010200143264007100245300003900316336002600355337002600381338003600407490005900443500001300502505123000515520100301745650001802748700002802766856005502794932003202849596000602881949010502887CR9780511550706UkCbUP090511s2004||||enk o ||1 0|eng|d a9780511550706 a9780521542876 a(Sirsi) a792512 aeng00a512/.222200aGroups :btopological, combinatorial, and arithmetic aspectsh[E-Book] /cedited by T.W. Müller. 1aCambridge :bCambridge University Press,c2004e(CUP)fCUP20200108 a1 online resource (xvi, 587 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier aLondon Mathematical Society lecture note series ;v311 aenglisch0 a1. 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. Müller -- 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 -- 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. aIn 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. 0aGroup theory.1 aMüller, T. W.,eeditor40uhttps://doi.org/10.1017/CBO9780511550706zVolltext aCambridgeCore (Order 30059) a1 aXX(792512.1)wAUTOc1i792512-1001lELECTRONICmZBrNsYtE-BOOKu8/1/2020xUNKNOWNzUNKNOWN1ONLINE