Summer School in Group Theory in Banff, 1996Olga Kharlampovich The third annual CRM Summer School took place in Banff (Alberta, Canada) and was aimed toward advanced students and recent PhDs. This volume presents surveys from the group theory part of the theme year and examines different approaches to the topic: a geometric approach, an approach using methods from logic, and an approach with roots in the Bass-Serre theory of groups acting on trees. The work offers a concise introduction to current directions of research in combinatorial group theory. Surveys in the text are by leading researchers in the field who are experienced expositors. The text is suitable for use in a graduate course in geometric and combinatorial group theory. |
Contents
Some Open Problems | 1 |
Length Functions and ATrees | 11 |
Introduction to Hyperbolic and Automatic Groups | 45 |
Description of Fully Residually Free Groups and Irreducible Affine Varieties Over a Free Group | 71 |
Homological Methods in Group Theory | 81 |
Prop Groups | 99 |
Identities of Representations of Finite Groups | 131 |
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Common terms and phrases
0-hyperbolic A-tree analytic groups automorphism basis of identities Bass-Serre theory Baumslag called Cayley graph central extension combinatorial commutative Corollary cyclic group d-identities defined definition Dehn function denote edges elements equationally Noetherian equations equivalent exact sequence example finite basis finite group finite set finitely generated group finitely presented follows free abelian groups free group free product fully residually free Galois group graph of groups group G group theory groups of order Hence homology homomorphism hyperbolic groups inverse irreducible isometries isomorphic Lemma length function Let G Lie algebra linear lower p-series Lyndon Math maximal metric space Myasnikov normal subgroup one-relator groups ordered abelian group p-group power series pro-p group problem profinite group proof Proposition proved quadratic quotient R-analytic R-standard R-tree Remeslennikov representation residually free group satisfies segment Shalev standard groups structure subset subtree TG,A Theorem topology torsion-free tree vertex ZG-module