Basic Algebra

Introduction to Group Theory Introduction to Group Theory- A fairly easy to understand tutorial. Fourteen sections, including groups, Cayley tables, subgroups, cosets, Lagrange's theorem, cyclic groups and su… Symmetry 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 h… Group Theory 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. Semigroup Theory Semigroup Theory- Directory of home pages and conferences maintained at Southampton University. Topological Methods in Group Theory Topological Methods in Group Theory- Table of contents only; draft chapters can be downloaded by arrangement. Common Systems of Coset Representatives 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 Dharwa… Abstract groups Abstract groups- The abstract group concept. Material based on lectures by Peter Neumann. Computational Tools for Group Theory 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 Tabl… The Lie algebras su(N), an introduction 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. Group Theory Group Theory- On-line book by Prederic Cvitanovic. Available both in 'psd' and 'ps' formats. Group Action Forum Group Action Forum- Association for the study of the theory of transformation groups and related topics. Members, news, events, publications. Broue's Abelian Defect Group Conjecture Broue's Abelian Defect Group Conjecture- A record of which groups and blocks have been proved to satisfy the conjecture, maintained by Jeremy Rickard. PARGAP PARGAP- Parallel GAP/MPI (ParGAP/MPI), a share package for GAP. UNIX (or Cygwin/Windows). Download source and documentation by FTP. Binary Coordinate Systems Binary Coordinate Systems- Article by Steven H. Cullinane. Defines "Cartesian" coordinate systems for small finite geometries over the two-element field, and discusses geometrical… Trinomials with Interesting Galois Groups Trinomials with Interesting Galois Groups- Parametrisation of trinomials with Galois groups contained in the simple group G168. Papers by R. E. Borcherds Papers by R. E. Borcherds- Including proof of the Moonshine Conjecture (TeX, DVI, PDF). Permutation Groups Resources Permutation Groups Resources- Web-based resources for permutation groups and related areas in group theory and combinatorics. Permutation Group Problems Permutation Group Problems- Compiled by Peter Cameron. GAP - Groups, Algorithms and Programming GAP - Groups, Algorithms and Programming- GAP is a free system for computational discrete algebra. International Society for Group Theory in Cognitive Science International Society for Group Theory in Cognitive Science- Group theory in: Robotics, Problem-Solving, Planning, Learning, Language, Perception, Art, Design, Engineering, Manufa… Coxeter/Weyl Tutorial 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 Group Pub Forum Home Page 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… ArXiv Front: GR Group Theory ArXiv Front: GR Group Theory- Group theory section of the mathematics e-print arXiv.