GAP is a system for discrete computational algebra.

ATLAS of Finite Group Representations Version 1 This ATLAS of Group Representations has been prepared by Robert Wilson, Peter Walsh, Jonathan Tripp, Ibrahim Suleiman, Stephen Rogers, Richard Parker, Simon Norton, Steve Linton and John Bray (in reverse alphabetical order, because I'm fed up with always being last!). Version 1 This website has been under continuous development for several years ...

Symmetric Presentations Well, my research is in group theory which is a part of algebra. In particular, I study symmetric presentations. If you don't know what a group is then click here for a definition. If the reader seeks a representation of a group, then he should refer to the ATLAS of group representations which is maintained by R.A.Wilson and R.A.Parker. We shall give some presentations of ...

New York Group Theory Cooperative Enter Here | Domain Name Registration and Domain Name Forwarding by NamesDirect.com - Register your domain name. ...

Web-based resources for permutation groups and related areas ...

GT-CS International Society for Group Theory in Cognitive Science BB Society President: Michael Leyton (USA) Eloise Carlton (USA), Vladimir Dorodnitsyn (Russia), Roy Eagleson (Canada), Mario Ferraro (Italy), Victor Finn (Russia), Nathaniel Friedman (USA), Ted Goranson (USA), Bill Hammel (USA), Slavik Jablan (Jugoslavia), Vladimir Koptsik (Russia), Joan Lasenby (UK), Yanxi Liu (USA), Guerino ...

THE MOD-2 COHOMOLOGY OF 2-GROUPS On this web page we present the data from the first run of the computer calculation of the mod-2 cohomology of groups of order 8, 16, 32 and 64. to see the results of the second run click here.. All of the calculations were run using the MAGMA computer algebra system. The groups are indexed by their Hall-Senior Numbers. State of the Calculation The first run was ...

Research problems on permutation groups, with commentary ...

A Tutorial Introduction to the Coxeter and Weyl Packages Contents Introduction Vectors Root Systems The Database Commands Group Elements Permutation Representations Group Characters Weight Vectors Weyl Characters Using the Examples Introduction This document provides a step-by-step introduction to the use of Version 2.1 of coxeter and weyl, a pair of Maple packages for working with root systems, ...

Parallel GAP/MPI (ParGAP/MPI), a share package for GAP This package works only under UNIX. (Cygwin is an option on Windows, but you will have to port it, then.) The most recent version of this package can always be found in the ParGAP ftp directory. You can also find ParGAP/MPI at the web page for GAP share packages. A good introduction to ParGAP is available as a preprint in either gzipped ...

Groups of small order Compiled by John Pedersen, Dept of Mathematics, University of South Florida, jfp@math.usf.edu Order 1 and all prime orders (1 group: 1 abelian, 0 nonabelian) All groups of prime order p are isomorphic to C_p, the cyclic group of order p. A concrete realization of this group is Z_p, the integers under addition modulo p. Order 4 (2 groups: 2 abelian, 0 nonabelian) C_4, the ...

Binary Coordinate Systems by Steven H. Cullinane (Article intended for American Mathematical Monthly readers, written July 1984) Mathematics Subject Classification (MSC2000) - Primary: 20B25, Finite automorphism groups of algebraic, geometric, or combinatorial structures. Secondary: 05B25, Finite geometries; 51E20, Combinatorial structures in finite projective spaces. This article tells how to ...

Finite groups in MAPLE5 The elements and group table of a permutation group Conjugacy classes of a permutation group Right and left cosets of a permutation group Elements of a given order of a permutation group The action of the permutation group G on {1, 2, ..., degree(G)} Representation-theoretic commands This worksheet contains programs to list all the elements of a permgroup as disjoint cycles ...

Collapsed Adjacency Matrices, Character Tables and Ramanujan Graphs This is a database of character tables of endomorphism rings. Let G be a finite group, K a field and M a finite set on which G acts transitively. For a in M let M1={a}, M2, ..., Mr be the distinct orbits of Ga, which have respective representatives a1=a, a2, ..., ar. Let Ei be an orbital for G as a subset of MxM. For 1 &lt= i &lt= r ...

Trinomials axn+bx+c with interesting Galois groups In 1969 Trinks discovered that the irreducible trinomial x7 - 7 x + 3, factored modulo small primes (other than the primes 3 and 7 dividing its discriminant 218), always yielded polynomials of degrees 7, 4+2+1, 3+3+1, or 2+2+1+1+1. This suggested that the trinomial had Galois group G168, the simple group of order 168 consisting of the invertible ...