Group Theory

Abstract groups :

- The abstract group concept. Material based on lectures by Peter Neumann.
ArXiv Front: GR Group Theory :

- Group theory section of the mathematics e-print arXiv.
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.
Broue's Abelian Defect Group Conjecture :

- A record of which groups and blocks have been proved to satisfy the conjecture, maintained by Jeremy Rickard.
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.
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.
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
GAP - Groups, Algorithms and Programming :

- GAP is a free system for computational discrete algebra.
Group Action Forum :

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

- On-line book by Prederic Cvitanovic. Available both in 'psd' and 'ps' formats.
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.
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.
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.
Mod-2 Cohomology of 2-Groups :

- Computer calculation of the mod-2 cohomology of groups of order 8, 16, 32 and 64.
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.
Open Problems in Group Theory :

- Part of the Magnus project. Contains over 150 problems in group theory, both well known and relatively new.
Papers by R. E. Borcherds :

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

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

- Compiled by Peter Cameron.
Permutation Groups Resources :

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

- Some presentations of groups (symmetric or otherwise).
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.
Symmetry Groups in Maple V :

- A worksheet by W.D. Joyner.
Trinomials with Interesting Galois Groups :

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