Finite Groups

Groups

General group creation and standard group extension constructors.

Groups

Permutation Groups

Permutation group constructors, operations and homomorphisms.

Permutation Groups

Matrix Groups over General Rings

General linear group creation, homomorphisms and element operations.

Matrix Groups over General Rings

Matrix Groups over Finite Fields

Element order, Monte Carlo methods and Aschbacher reduction.

Matrix Groups over Finite Fields

Matrix Groups over Infinite Fields

Congruence, finiteness and virtual membership tests.

Matrix Groups over Infinite Fields

Matrix Groups over Q and Z

Invariant forms, endomorphisms and related constructions.

Matrix Groups over Q and Z

Finite Soluble Groups

PC-group definition, properties and homomorphisms.

Finite Soluble Groups

Black-box Groups

Black-box group creation, operations and element operations.

Black-Box Groups

Almost Simple Groups

Double covers, standard constructions and group recognition.

Almost Simple Groups

Databases of Groups

Small groups, simple groups and p-group databases.

Databases of Groups

Automorphism Groups

Automorphism group creation, access and order.

Automorphism Groups

Cohomology and Extensions

Cohomology groups, structural invariants and group extensions.

Cohomology and Extensions

Reductive Groups

Reductive group creation, properties and operations.

Reductive Groups