This package contains three methods to construct the groups of a certain type up to isomorphism.

**The Frattini Extension Method**:

This method can be used to determine all soluble groups of a given order. The practicability of the method depends clearly on the chosen order. Furthermore, the efficiency of the method might be increased by restricting the construction to groups with certain properties. This is easily possible for a number of properties; for example, it is useful and straightforward to compute non-nilpotent groups only. (See Chapter The Frattini Extension Method.)

**The Cyclic Split Extension Method**:

The cyclic split extension method can be used to list all groups of
order `p ^{n} cdotq` for different primes

**The Upwards Extension Method**:

The upwards extension method is the most general of the three methods. It can be used to construct all groups of a given order. However, it is the least efficient of the three methods and hence should only be used to construct non-soluble groups. Note that this method needs a list of perfect groups of order dividing the given one. (See Chapter The Upwards Extension Method.)

Furthermore, the package contains a wrap up function which combines
the three methods to a general algorithm to construct the groups of
a given order. (See Chapter Construction of All Groups.) Finally,
there is an info class `InfoGrpCon`

available for the functions of
this share package with possible levels 1 up to 4.

[Up] [Previous] [Next] [Index]

grpconst manual

Mai 2012