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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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 the 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.

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.

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.

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.

Semigroup Theory

Directory of home pages and conferences maintained at Southampton University.

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.

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.

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