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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.
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