Abstract Algebra Algebra Algebraic Geometry Algebraic Topology Applied Mathematics Arithmetic Geometry Basic Algebra Basic Mathematics Calculus Category Theory Classical Analysis Combinatorics Commutative Algebra Complex Algebra Complex Analysis Differential Algebra Differential Analysis Differential Calculus Differential Equations Differential Geometry Differential Topology Discrete Mathematics Elliptic Curves Fourier Analysis Functional Analysis Fractals Fractional Calculus Geometric Algebra Geometry Geometric Topology Groups Theory Graph Theory Harmonic Analysis Higher Algebra History of Mathematics Homological Algebra Integral Calculus K-theory Lie Algebra Linear Algebra Mathematical Analysis Mathematical Series Modern Geometry Multivairable Calculus Number Theory Numerical Analysis Probability Theory Real Analysis Rings and Fileds Riemannian Geometry Theorems in Calculus Topology Trigonometry Set Theory Constants & Numerical Sequences
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
126Pages
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
817Pages
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
103Pages
This explains the following topics: Free groups and presentations, Construction of new groups, Properties, embeddings and examples, Subgroup Theory and Decision Problems.
Author(s): Charles F. Miller
99Pages
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