Group Theory

Abstract groups
The abstract group concept. Material based on lectures by Peter Neumann.
http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Abstract_groups.html

ArXiv Front: GR Group Theory
Group theory section of the mathematics e-print arXiv.
http://front.math.ucdavis.edu/math.GR

Binary Coordinate Systems
Article by Steven H. Cullinane. Defines "Cartesian" coordinate systems for small finite geometries over the two-element field, and discusses geometrically simple generators for affine group actions.
http://m759.freeservers.com/coord.html

Broue's Abelian Defect Group Conjecture
A record of which groups and blocks have been proved to satisfy the conjecture, maintained by Jeremy Rickard.
http://www.maths.bris.ac.uk/~majcr/adgc/adgc.html

Common Systems of Coset Representatives
Proof of existence of a common system of representatives for the left and right cosets of a finite subgroup of a group by Ashay Dharwadker.
http://www.geocities.com/dharwadker/coset.html

Computational Tools for Group Theory
Describes work to create a program that could be used to generate, identify, and analyze finite groups presented in the form of a Cayley Table as well as visualize the groups that are generated.
http://www.groovypower.com/thesis/

Coxeter/Weyl Tutorial
A Tutorial Introduction to the Coxeter and Weyl Packages, a pair of Maple packages for working with root systems, finite Coxeter groups and Weyl characters
http://www.math.lsa.umich.edu/~jrs/coxtut.html

GAP - Groups, Algorithms and Programming
GAP is a free system for computational discrete algebra.
http://www.gap-system.org/

Group Action Forum
Association for the study of the theory of transformation groups and related topics. Members, news, events, publications.
http://gaf.astagor.net/

Group Pub Forum Home Page
These are the community pages for Group Theory, the mathematics of symmetry. Group Theory is a branch of algebra, but has strong connections with almost all parts of mathematics.
http://www.bath.ac.uk/~masgcs/gpf.html

Group Theory
On-line book by Prederic Cvitanovic. Available both in 'psd' and 'ps' formats.
http://www.nbi.dk/GroupTheory/

International Society for Group Theory in Cognitive Science
Group theory in: Robotics, Problem-Solving, Planning, Learning, Language, Perception, Art, Design, Engineering, Manufacturing, Epistemology, Measurement, Computation, Neuroscience, Anthropology, Semiotics.
http://www.rci.rutgers.edu/~mleyton/GT.htm

Introduction to Group Theory
A fairly easy to understand tutorial. Fourteen sections, including groups, Cayley tables, subgroups, cosets, Lagrange's theorem, cyclic groups and subgroups, permutations, and Rubik's cube.
http://members.tripod.com/dogschool/

The Lie algebras su(N), an introduction
Publication: An Introduction to the Lie Algebras su(N). By Walter Pfeifer, Switzerland. A free copy can be ordered.
http://lie.walterpfeifer.ch/

Mod-2 Cohomology of 2-Groups
Computer calculation of the mod-2 cohomology of groups of order 8, 16, 32 and 64.
http://www.math.uga.edu/~jfc/groups/cohomology.html

New York Group Theory Cooperative
Software (Magnus), preprints, meetings, links. Magnus - a graphically-oriented system for computational group theory - allows one to explore and experiment with abstract groups without the need for learning yet another programming language. Magnus is freely available software (GPL) based on Tcl/Tk.
http://zebra.sci.ccny.cuny.edu/web/

Open Problems in Group Theory
Part of the Magnus project. Contains over 150 problems in group theory, both well known and relatively new.
http://zebra.sci.ccny.cuny.edu/web/nygtc/problems/

Papers by R. E. Borcherds
Including proof of the Moonshine Conjecture (TeX, DVI, PDF).
http://math.berkeley.edu/~reb/papers/

PARGAP
Parallel GAP/MPI (ParGAP/MPI), a share package for GAP. UNIX (or Cygwin/Windows). Download source and documentation by FTP.
http://www.ccs.neu.edu/home/gene/pargap.html

Permutation Group Problems
Compiled by Peter Cameron.
http://www.maths.qmw.ac.uk/~pjc/pgprob.html

Permutation Groups Resources
Web-based resources for permutation groups and related areas in group theory and combinatorics.
http://www.maths.qmw.ac.uk/~pjc/permgps/

Symmetry
The main point group symmetries of interest to defect physics by operation (reflection, rotations etc) and classification (trigonal, and cubic). Most point groups also have the associated character table on-line.
http://newton.ex.ac.uk/research/qsystems/people/goss/symmetry/index.html

Symmetry Groups in Maple V
A worksheet by W.D. Joyner.
http://web.usna.navy.mil/~wdj/symm_gp.html

Trinomials with Interesting Galois Groups
Parametrisation of trinomials with Galois groups contained in the simple group G168.
http://www.math.harvard.edu/~elkies/trinomial.html

The World of Groups
Part of the World Wide Algebra project. Open problems in combinatorial group theory, a list of personal web pages, conferences and seminars, and useful links.
http://www.cs.gc.cuny.edu/~cryptlab/gworld/gworld.html