In this chapter, we consider a class of finitely presented groups for which the word problem is solvable, the category of -- possibly infinite -- polycyclic groups. The corresponding Magma category is called GrpGPC. To distinguish this class from finite solvable groups described by a power-conjugate presentation (Magma category GrpPC, cf. Chapter FINITE SOLUBLE GROUPS), we use the term general polycyclic group.
An introduction to the theory of polycyclic groups and a collection of some basic algorithms can be found in [Sim94, ch. 9]. Unless otherwise mentioned, implementations of Magma functions are mostly based on ideas described in this reference.