Group theory section of the mathematics e-print arXiv.

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.

Table of contents only; draft chapters can be downloaded by arrangement.

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

A worksheet by W.D. Joyner.

Group theory in: Robotics, Problem-Solving, Planning, Learning, Language, Perception, Art, Design, Engineering, Manufacturing, Epistemology, Measurement, Computation, Neuroscience, Anthropology, Semiotics.

Computer calculation of the mod-2 cohomology of groups of order 8, 16, 32 and 64.

GAP is a free system for computational discrete algebra.

Bibliography, meetings.

Compiled by Peter Cameron.

Web-based resources for permutation groups and related areas in group theory and combinatorics.

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.

Including proof of the Moonshine Conjecture (TeX, DVI, PDF).

Parametrisation of trinomials with Galois groups contained in the simple group G168.

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.

Parallel GAP/MPI (ParGAP/MPI), a share package for GAP. UNIX (or Cygwin/Windows). Download source and documentation by FTP.

Part of the Magnus project. Contains over 150 problems in group theory, both well known and relatively new.

A record of which groups and blocks have been proved to satisfy the conjecture, maintained by Jeremy Rickard.

Some presentations of groups (symmetric or otherwise).

Association for the study of the theory of transformation groups and related topics. Members, news, events, publications.

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.

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.

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.

On-line book by Prederic Cvitanovic. Available both in 'psd' and 'ps' formats.

Publication: An Introduction to the Lie Algebras su(N). By Walter Pfeifer, Switzerland. A free copy can be ordered.

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.

The abstract group concept. Material based on lectures by Peter Neumann.

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.