# Introduction

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](../../FiniteGroups/FiniteSolubleGroups/index-finite-soluble-groups.md#chapgrppc)), 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 [[Sims, 1994](../../references.md#cite-sims-fpgroups), ch. 9]. Unless otherwise mentioned, implementations of Magma functions are mostly based on ideas described in this reference.