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

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