Group Theory

Abstract groups - The abstract group concept. Material based on lectures by Peter Neumann.
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.
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.
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.
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.
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.
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
www.math.lsa.umich.edu/~jrs/coxtut.html

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

Group Action Forum - Association for the study of the theory of transformation groups and related topics. Members, news, events, publications.
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.
www.bath.ac.uk/~masgcs/gpf.html

Group Theory - On-line book by Prederic Cvitanovic. Available both in 'psd' and 'ps' formats.
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.
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.
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.
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.
www.math.uga.edu/~jfc/groups/cohomology.html

The Moonshine Page - Bibliography, meetings.
cicma.mathstat.concordia.ca/faculty/cummins/moonshine.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.
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.
zebra.sci.ccny.cuny.edu/web/nygtc/problems/

Papers by R. E. Borcherds - Including proof of the Moonshine Conjecture (TeX, DVI, PDF).
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.
www.ccs.neu.edu/home/gene/pargap.html

Permutation Group Problems - Compiled by Peter Cameron.
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.
www.maths.qmw.ac.uk/~pjc/permgps/

Semigroup Theory - Directory of home pages and conferences maintained at Southampton University.
www.maths.soton.ac.uk/semigroups/homepage.html

Symmetric Presentations - Some presentations of groups (symmetric or otherwise).
web.mat.bham.ac.uk/J.N.Bray/res.html

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.
newton.ex.ac.uk/research/qsystems/people/goss/symmetry/index.html

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

Topological Methods in Group Theory - Table of contents only; draft chapters can be downloaded by arrangement.
www.math.binghamton.edu/ross/contents.html

Trinomials with Interesting Galois Groups - Parametrisation of trinomials with Galois groups contained in the simple group G168.
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.
www.cs.gc.cuny.edu/~cryptlab/gworld/gworld.html