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 Science > Math > Algebra > Group Theory

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Science > Math > Algebra > Group Theory

Group Theory:

Abstract groups

The abstract group concept. Material based on lectures by Peter Neumann.

http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Abstract_groups.html

ArXiv Front: GR Group Theory

Group theory section of the mathematics e-print arXiv.

http://front.math.ucdavis.edu/math.GR

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.

http://m759.freeservers.com/coord.html

Graand

Free Classified Ads Portal

www.graand.com

Broue's Abelian Defect Group Conjecture

A record of which groups and blocks have been proved to satisfy the conjecture, maintained by Jeremy Rickard.

http://www.maths.bris.ac.uk/~majcr/adgc/adgc.html

Common Systems of Coset Representatives

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.

http://www.geocities.com/dharwadker/coset.html

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.

http://www.groovypower.com/thesis/

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

http://www.math.lsa.umich.edu/~jrs/coxtut.html

GAP - Groups, Algorithms and Programming

GAP is a free system for computational discrete algebra.

http://www.gap-system.org/

Group Action Forum

Association for the study of the theory of transformation groups and related topics. Members, news, events, publications.

http://gaf.astagor.net/

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.

http://www.bath.ac.uk/~masgcs/gpf.html

Group Theory

On-line book by Prederic Cvitanovic. Available both in 'psd' and 'ps' formats.

http://www.nbi.dk/GroupTheory/

Group Theory

Group theory in: Robotics, Problem-Solving, Planning, Learning, Language, Perception, Art, Design, Engineering, Manufacturing, Epistemology, Measurement, Computation, Neuroscience, Anthropology, Semiotics.

http://www.rci.rutgers.edu/~mleyton/GT.htm

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.

http://members.tripod.com/dogschool/

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.

http://lie.walterpfeifer.ch/

Mod-2 Cohomology of 2-Groups

Computer calculation of the mod-2 cohomology of groups of order 8, 16, 32 and 64.

http://www.math.uga.edu/~jfc/groups/cohomology.html

New York Group Theory Cooperative

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.

http://zebra.sci.ccny.cuny.edu/web/

Open Problems in Group Theory

Part of the Magnus project. Contains over 150 problems in group theory, both well known and relatively new.

http://zebra.sci.ccny.cuny.edu/web/nygtc/problems/

Papers by R. E. Borcherds

Including proof of the Moonshine Conjecture (TeX, DVI, PDF).

http://math.berkeley.edu/~reb/papers/

PARGAP

Parallel GAP/MPI (ParGAP/MPI), a share package for GAP. UNIX (or Cygwin/Windows). Download source and documentation by FTP.

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

Permutation Group Problems

Compiled by Peter Cameron.

http://www.maths.qmw.ac.uk/~pjc/pgprob.html

Permutation Groups Resources

Web-based resources for permutation groups and related areas in group theory and combinatorics.

http://www.maths.qmw.ac.uk/~pjc/permgps/

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.

http://newton.ex.ac.uk/research/qsystems/people/goss/symmetry/index.html

Symmetry Groups in Maple V

A worksheet by W.D. Joyner.

http://web.usna.navy.mil/~wdj/symm_gp.html

Trinomials with Interesting Galois Groups

Parametrisation of trinomials with Galois groups contained in the simple group G168.

http://www.math.harvard.edu/~elkies/trinomial.html

The World of Groups

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.

http://www.cs.gc.cuny.edu/~cryptlab/gworld/gworld.html