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Notes on Group Theory by Mark Reeder
This note covers Notation for sets and functions, Basic group theory, The symmetric group, Group actions, Linear groups, Affine groups, Projective groups, Abelian groups, Finite linear 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
127 Pages
Geometric Group Theory Preliminary Version Under revision
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
This note explains the following topics: Simple groups, Examples of groups, Group actions, Sylow’s Theorem, Group extensions, Soluble and nilpotent groups, Symmetric and alternating groups, Linear groups.
Author(s): Peter J. Cameron
103 Pages
Group Theory Lecture Notes (PDF 88P)
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The Classification of the Finite Simple Groups
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Homogeneous spaces and equivariant embeddings
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