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Group Theory

Science > Math > Algebra > Group Theory

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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.

Algebra and Representation Theory in the North (ARTIN) - http://www.maths.abdn.ac.uk/artin/
List of future meetings in the United Kingdom and details of past meetings.

ArXiv Front: GR Group Theory - http://front.math.ucdavis.edu/math.GR
Group theory section of the mathematics e-print arXiv.

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.

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.

Common Systems of Coset Representatives - http://www.dharwadker.org/coset.html
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 - 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.

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

GAP - Groups, Algorithms and Programming - http://www.gap-system.org/
GAP is a free system for computational discrete algebra.

Group Action Forum - http://gaf.astagor.net/
Association for the study of the theory of transformation groups and related topics. Members, news, events, publications.

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.

Group Theory - http://www.nbi.dk/GroupTheory/
On-line book by Prederic Cvitanovic. Available both in 'psd' and 'ps' formats.

Group Theory - http://en.wikipedia.org/wiki/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.

http://www.ccs.neu.edu/home/gene/pargap.html - 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.

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.

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.

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.

Papers by R. E. Borcherds - http://math.berkeley.edu/~reb/papers/
Including proof of the Moonshine Conjecture (TeX, DVI, PDF).

Permutation Group Problems - http://www.maths.qmw.ac.uk/~pjc/pgprob.html
Compiled by Peter Cameron.

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.

Semigroup Theory - http://www.personal.soton.ac.uk/jhr/semigroups/
Directory of home pages and conferences maintained at Southampton University.

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 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.

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.

Topological Methods in Group Theory - http://math.binghamton.edu/ross/contents.html
Table of contents only; draft chapters can be downloaded by arrangement.

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.

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