26.7 Ag Group Functions for Special Ag Groups

Since special ag groups are ag groups all functions for ag groups are applicable to special ag groups. However certain of these functions use special implementations to treat special ag groups, i.e. there exists functions like SagGroupOps.FunctionName, which are called by the corresponding general function in case a special ag group given. If you call one of these general functions with an arbitrary ag group, the general function will not calculate the special ag group but use the function for ag groups. For the special implementations to treat special ag groups note the following.

Centre( H )
MinimalGeneratingSet( H )
Intersection( U, L)
EulerianFunction( H ) MaximalSubgroups( H )
ConjugacyClassesMaximalSubgroups( H )
PrefrattiniSubgroup( H )
FrattiniSubgroup( H )
IsNilpotent( H )
These functions are often faster and often use less space for special ag groups.

ElementaryAbelianSeries( H )
More about Special Ag Groups).

IsElementaryAbelianSeries( H )
Returns true.

HallSubgroup( H, primes )
SylowSubgroup( H, p )
SylowSystem( H )
More about Special Ag Groups).

Subgroup( H, gens )
AgSubgroup( H, gens, bool )
These functions return an ag group which is not special, except if the group itself is returned.

All domain functions not mentioned here use no special treatments for special ag groups.

Note also that there exists a package to compute formation theoretic subgroups of special ag groups. This may be used to compute the system normalizer of the public Sylow system, which is the F-normalizer for the formation of nilpotent groups F. It is also possible to compute F-normalizers as well as F-covering subgroups and F-residuals of special ag groups for a number of saturated formations F which are given within the package or for self-defined saturated formations F. Previous Up Top
Index

GAP 3.4.4
April 1997