Databases of Structure Definitions

These are Magma's databases of structure definitions.

Polynomials with given Galois groups. For each transitive group G with degree between 2 and 11, the database contains a univariate polynomial over the integers which has G as its Galois group.

isolgps

The irreducible soluble subgroups of GL(n, p) for n > 1 and p^n < 256.

matgps

Various useful matrix groups, almost all over finite fields (the only exception is the Weyl group E6).

pergps

A number of permutation representations for finite groups. A particular group is included either if (a) It is an "interesting" group. In practice this means a simple group or a close relative of a simple group; or (b) It is representative of some class of groups which is useful for testing conjectures and algorithms.

simgps

Presentations for all simple groups of order less than a million. The database was prepared by Jamali, Robertson and Campbell.

solgps

Power-conjugate presentations of 13 soluble groups constructed by S.P. Glasby.

Magma also has a library of files containing functions and procedures written in the Magma language. See Libraries of Functions in the Magma Language.

Subscreens

• Database of Galois Group Polynomials
• Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256
• Database of Matrix Groups
• Database of Some Permutation Groups
• Database of Simple Groups: Permutations, Presentations, Conjugacy Classes, Maximal Subgroups and Sylow Subgroups
• Database of Soluble Groups

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