GAP Manual: 26. Special Ag Groups

Special ag groups are a subcategory of ag groups (see 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 a special ag group than for an arbitrary one. (See Ag Group Functions for Special Ag Groups)

The following sections describe the special ag system (see More about Special Ag Groups), their construction in GAP (see 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).

This chapter contains the following sections: