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Sponsored Links:
Introduction to Group Theory (Popularity:  )
http://members.tripod.com/dogschool/
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.
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GAP - Groups, Algorithms and Programming (Popularity: )
http://www.gap-system.org/
GAP is a free system for computational discrete algebra.
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Group Pub Forum Home Page (Popularity: )
http://www.bath.ac.uk/~masgcs/gpf.html
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.
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Permutation Group Problems (Popularity: )
http://www.maths.qmw.ac.uk/~pjc/pgprob.html
Compiled by Peter Cameron.
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ArXiv Front: GR Group Theory (Popularity: )
http://front.math.ucdavis.edu/math.GR
Group theory section of the mathematics e-print arXiv.
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International Society for Group Theory in Cognitive Science (Popularity: )
http://www.rci.rutgers.edu/~mleyton/GT.htm
Group theory in: Robotics, Problem-Solving, Planning, Learning, Language, Perception, Art, Design, Engineering, Manufacturing, Epistemology, Measurement, Computation, Neuroscience, Anthropology, Semiotics.
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Coxeter/Weyl Tutorial (Popularity: )
http://www.math.lsa.umich.edu/~jrs/coxtut.html
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
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Topological Methods in Group Theory (Popularity: )
http://www.math.binghamton.edu/ross/contents.html
Table of contents only; draft chapters can be downloaded by arrangement.
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Broue's Abelian Defect Group Conjecture (Popularity: )
http://www.maths.bris.ac.uk/~majcr/adgc/adgc.html
A record of which groups and blocks have been proved to satisfy the conjecture, maintained by Jeremy Rickard.
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Permutation Groups Resources (Popularity: )
http://www.maths.qmw.ac.uk/~pjc/permgps/
Web-based resources for permutation groups and related areas in group theory and combinatorics.
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Mod-2 Cohomology of 2-Groups (Popularity: )
http://www.math.uga.edu/~jfc/groups/cohomology.html
Computer calculation of the mod-2 cohomology of groups of order 8, 16, 32 and 64.
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Binary Coordinate Systems (Popularity: )
http://m759.freeservers.com/coord.html
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.
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Papers by R. E. Borcherds (Popularity: )
http://math.berkeley.edu/~reb/papers/
Including proof of the Moonshine Conjecture (TeX, DVI, PDF).
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Group Action Forum (Popularity: )
http://gaf.astagor.net/
Association for the study of the theory of transformation groups and related topics. Members, news, events, publications.
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Collapsed Adjacency Matrices, Character Tables and Ramanujan Graphs (Popularity: )
http://www.math.rwth-aachen.de/~Ines.Hoehler/
A database of character tables of endomorphism rings.
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Trinomials with Interesting Galois Groups (Popularity: )
http://www.math.harvard.edu/~elkies/trinomial.html
Parametrisation of trinomials with Galois groups contained in the simple group G168.
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Symmetry (Popularity: )
http://newton.ex.ac.uk/research/qsystems/people/goss/symmetry/index.html
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.
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PARGAP (Popularity: )
http://www.ccs.neu.edu/home/gene/pargap.html
Parallel GAP/MPI (ParGAP/MPI), a share package for GAP. UNIX (or Cygwin/Windows). Download source and documentation by FTP.
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Groups of Small Order (Popularity: )
http://www.math.usf.edu/~eclark/algctlg/small_groups.html
A list of isomorphism classes and further information on groups of order up to 30, by John Pedersen, University of South Florida.
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The World of Groups (Popularity: )
http://www.cs.gc.cuny.edu/~cryptlab/gworld/gworld.html
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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