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..

Topological Methods in Group Theory - Table of contents only; draft chapters can be downloaded by arrangement..

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..

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