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Notes on Group Theory

This note covers the following topics: Notation for sets and functions, Basic group theory, The Symmetric Group, Group actions, Linear groups, Affine Groups, Projective Groups, Finite linear groups, Abelian Groups, Sylow Theorems and Applications, Solvable and nilpotent groups, p-groups, a second look, Presentations of Groups, Building new groups from old.

Author(s): Mark Reeder

126 Pages

The goal of this book is to present several central topics in geometric group theory, primarily related to the large scale geometry of infinite groups and spaces on which such groups act, and to illustrate them with fundamental theorems such as Gromov�s Theorem on groups of polynomial growth. Topics covered includes: Geometry and Topology, Metric spaces, Differential geometry, Hyperbolic Space, Groups and their actions, Median spaces and spaces with measured walls, Finitely generated and finitely presented groups, Coarse geometry, Coarse topology, Geometric aspects of solvable groups, Gromov�s Theorem, Amenability and paradoxical decomposition, Proof of Stallings� Theorem using harmonic functions.

Author(s): Cornelia Drutu and Michael Kapovich

817 Pages

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Notes on Group Theory

Notes on Group Theory

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