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.
Group Theory can be viewed as the
mathematical theory that deals with symmetry, where symmetry has a very general
meaning. This PDF book covers the following topics related to Group Theory :
Introduction, Definitions and basic properties, Direct products and abelian
groups, Composition series and solvable groups, Permutation groups and group
actions, Finite groups and Sylow Theory, Semidirect products and groups of order
less than 15.
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.
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,