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Group Theory

Science > Math > Algebra > Group Theory

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	GAP - Groups, Algorithms and Programming - http://www.gap-system.org/ GAP is a free system for computational discrete algebra.
	ArXiv Front: GR Group Theory - http://front.math.ucdavis.edu/math.GR Group theory section of the mathematics e-print arXiv.
	International Society for Group Theory in Cognitive Science - 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.
	Abstract groups - http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Abstract_groups.html The abstract group concept. Material based on lectures by Peter Neumann.
	Group Action Forum - http://gaf.astagor.net/ Association for the study of the theory of transformation groups and related topics. Members, news, events, publications.

	Open Problems in Group Theory - http://zebra.sci.ccny.cuny.edu/web/nygtc/problems/ Part of the Magnus project. Contains over 150 problems in group theory, both well known and relatively new.
	New York Group Theory Cooperative - http://zebra.sci.ccny.cuny.edu/web/ 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.
	Group Theory - http://www.nbi.dk/GroupTheory/ On-line book by Prederic Cvitanovic. Available both in 'psd' and 'ps' formats.
	Coxeter/Weyl Tutorial - 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
	Symmetric Presentations - http://web.mat.bham.ac.uk/J.N.Bray/res.html Some presentations of groups (symmetric or otherwise).

	Introduction to Group Theory - 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.
	Common Systems of Coset Representatives - http://www.geocities.com/dharwadker/coset.html 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.
	Mod-2 Cohomology of 2-Groups - 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.
	Topological Methods in Group Theory - http://www.math.binghamton.edu/ross/contents.html Table of contents only; draft chapters can be downloaded by arrangement.
	Permutation Groups Resources - http://www.maths.qmw.ac.uk/~pjc/permgps/ Web-based resources for permutation groups and related areas in group theory and combinatorics.

	Permutation Group Problems - http://www.maths.qmw.ac.uk/~pjc/pgprob.html Compiled by Peter Cameron.
	PARGAP - 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.
	Broue's Abelian Defect Group Conjecture - 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.
	Papers by R. E. Borcherds - http://math.berkeley.edu/~reb/papers/ Including proof of the Moonshine Conjecture (TeX, DVI, PDF).
	Binary Coordinate Systems - 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.

	Symmetry Groups in Maple V - http://web.usna.navy.mil/~wdj/symm_gp.html A worksheet by W.D. Joyner.
	Trinomials with Interesting Galois Groups - http://www.math.harvard.edu/~elkies/trinomial.html Parametrisation of trinomials with Galois groups contained in the simple group G168.
	The Lie algebras su(N), an introduction - http://lie.walterpfeifer.ch/ Publication: An Introduction to the Lie Algebras su(N). By Walter Pfeifer, Switzerland. A free copy can be ordered.
	Computational Tools for Group Theory - http://www.groovypower.com/thesis/ 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.
	Symmetry - 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.

	The World of Groups - 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.
	Group Pub Forum Home Page - 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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