In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. Groups recur throughout mathematics, and the methods of group theory have strongly influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced tremendous advances and have become subject areas in their own right.
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- ArXiv Front: GR Group Theory Group theory section of the mathematics e-print arXiv.
- 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.
- 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
- 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.
- GAP - Groups, Algorithms and Programming GAP is a free system for computational discrete algebra.
- Permutation Group Problems Compiled by Peter Cameron.
- Permutation Groups Resources Web-based resources for permutation groups and related areas in group theory and combinatorics.
- Papers by R. E. Borcherds Including proof of the Moonshine Conjecture (TeX, DVI, PDF).
- Trinomials with Interesting Galois Groups Parametrisation of trinomials with Galois groups contained in the simple group G168.
- 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.
- PARGAP Parallel GAP/MPI (ParGAP/MPI), a share package for GAP. UNIX (or Cygwin/Windows). Download source and documentation by FTP.
- Broue's Abelian Defect Group Conjecture A record of which groups and blocks have been proved to satisfy the conjecture, maintained by Jeremy Rickard.
- Group Action Forum Association for the study of the theory of transformation groups and related topics. Members, news, events, publications.
- Group Theory On-line book by Prederic Cvitanovic. Available both in 'psd' and 'ps' formats.
- 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.
- 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.
- Abstract groups The abstract group concept. Material based on lectures by Peter Neumann.
- Common Systems of Coset Representatives Proof of the existence of a common system of representatives for the left and right cosets of a finite subgroup of a group by Ashay Dharwadker.
- Topological Methods in Group Theory Table of contents only; draft chapters can be downloaded by arrangement.
- Semigroup Theory Directory of home pages and conferences maintained at Southampton University.
- Group Theory Information from Wikipedia on this concept, central to abstract algebra, its history, the main classes of groups and the applications of group theory.
- 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.
- 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.