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Introductory Group Theory Notes
This note explains the following topics: mapping, Basic algebra, Modular arithmetic, Groups, Cosets and Lagranges theorem, Isomorphisms and quotient group, The permutation group Sn, Finite abelian groups, Group actions, Group solvability and the semi direct product.
Author(s): Sumeet Khatri
216 Pages
Group Theory by Ferdi Aryasetiawan
This note describes the following topics: Abstract Group Theory, Theory of Group Representations, Group Theory in Quantum Mechanics, Lie Groups, Atomic Physics, The Group SU2: Isospin, The Point Groups, The Group SU3.
Author(s): Ferdi Aryasetiawan
140 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
