In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. Groups recur throughout mathematics, and the methods of group theory have strongly influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced tremendous advances and have become subject areas in their own right.
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The abstract group concept. Material based on lectures by Peter Neumann.
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.
A record of which groups and blocks have been proved to satisfy the conjecture, maintained by Jeremy Rickard.
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.
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 is a free system for computational discrete algebra.
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.
Information from Wikipedia on this concept, central to abstract algebra, its history, the main classes of groups and the applications of 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.
Including proof of the Moonshine Conjecture (TeX, DVI, PDF).
Parallel GAP/MPI (ParGAP/MPI), a share package for GAP. UNIX (or Cygwin/Windows). Download source and documentation by FTP.
Compiled by Peter Cameron.
Web-based resources for permutation groups and related areas in group theory and combinatorics.
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.
Table of contents only; draft chapters can be downloaded by arrangement.
Parametrisation of trinomials with Galois groups contained in the simple group G168.
Web-based resources for permutation groups and related areas in group theory and combinatorics.
Compiled by Peter Cameron.
The abstract group concept. Material based on lectures by Peter Neumann.
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.
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.
Information from Wikipedia on this concept, central to abstract algebra, its history, the main classes of groups and the applications of group theory.
Table of contents only; draft chapters can be downloaded by arrangement.
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.
Including proof of the Moonshine Conjecture (TeX, DVI, PDF).
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.
GAP is a free system for computational discrete algebra.
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.
Parallel GAP/MPI (ParGAP/MPI), a share package for GAP. UNIX (or Cygwin/Windows). Download source and documentation by FTP.
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
A record of which groups and blocks have been proved to satisfy the conjecture, maintained by Jeremy Rickard.
Parametrisation of trinomials with Galois groups contained in the simple group G168.
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October 16, 2023 at 5:25:12 UTC
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- Recently edited by cherel
- Recently edited by cherel