Finite Polycyclic Groups).
Let G be an ag group with PAG system (g_1, ldots, g_n). Then (g_1, ldots, g_n) is a special ag system if it is an ag system with some additional properties, which are described below.
In general a finite polycyclic group has several different ag systems and at least one of this is a special ag system, but in GAP an ag group is defined by a fixed ag system and according to this an ag group is called a special ag group if its ag system is a special ag system.
Special ag systems give more information about their corresponding group than arbitrary ag systems do (see More about Special Ag Groups) and furthermore there are many algorithms, which are much more efficient for Ag Group Functions for Special Ag Groups)
Construction of Special Ag Groups and Restricted Special Ag Groups) and their additional record entries (see Special Ag Group Records). Then follow two sections with functions which do only work for special ag groups (see MatGroupSagGroup and DualMatGroupSagGroup).