Topics in the Theory of Group Presentations
These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises have been added and the treatment of a number of topics has been improved and expanded. In addition, there are new chapters on the triangle groups, small cancellation theory and groups from topology. The connections between the theory of group presentations and other areas of mathematics are emphasized throughout. The book can be used as a text for beginning research students and, for specialists in other fields, serves as an introduction both to the subject and to more advanced treatises.
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Alexander polynomial algebra assume boundary label braid group called compute conjugates corresponding coset enumeration Coxeter group cyclic group deduce define denote direct product Dyck group elements epimorphism equal equation equivalent exact sequence Example EXERCISE 9 extension factor group Fibonacci Fibonacci groups Fig.l find a presentation finite p-group finite presentation follows free abelian group free group G-action G-homomorphism G-module given group G group of order group theory Hence homomorphism induction infinite integer inverses isomorphic Kampen diagram knot Lemma Let F Let G mapping matrix metacyclic groups method Nielsen-Schreier theorem normal closure normal subgroup obtain permutation prove reduced word respectively result Schreier transversal short exact sequence small cancellation subgroup H subgroup of G subset tangles Tietze transformations triangles trivial unique vertex vertices whence x e G yields
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