Algebraic Groups and Discontinuous Subgroups

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

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