Groups

Group theory has been one of the Computational Algebra Group's traditional strengths and Magma provides the user with access to nearly all of the significant algorithms for finite groups and finitely presented infinite groups (fp-groups). The important categories of group include:

• Permutation groups
• Matrix groups

• Finitely presented groups

• Generic abelian groups
• Finitely-presented abelian groups

• Polycyclic groups
• Soluble groups
• Finite p-groups

• Automorphism groups

• Groups defined by rewrite systems
• Automatic groups

• Groups with elements given as straight-line programs

• Braid groups

• Congruence subgroups of $PSL(2, \mbox{\bf R})$

In addition, Magma provides extensive machinery for the representation theory of groups which is discussed in the Representation Theory section of this document.