This chapter describes the Interface to the ANU Nilpotent Quotient
Program. Some functions rely on the functionality of the polycyclic
package and cannot be used if this package is not installed.
For easy reference, define the lowere central sreis of a group G by G1 = G and Gi+1 = [G,Gi] for i ³ 1·
The following functions are available and require the presence of the
polycyclic package.
NilpotentQuotient( fp group, class )
NilpotentQuotient( output filename, fp group, class )
NilpotentQuotient( input filename, class )
NilpotentQuotient( output filename, input filename, class )
This function computes a polycyclic presentation for G/Gc+1 where G is the finitely presented group fp group and c is the class specified by the parameter class. In other words, this function returns the largest nilpotent quotient of the finitely presented group fp group of class at most class.
EpimorphismNilpotentQuotient( fp group, class )
This function computes an epimorphism onto G/Gc+1· It requires the
presence of the polycyclic package.
LowerCentralFactors( fp group, class )
This function computes the abelian invariants of the factors of the lower central series of the given finitely presented group up to nilpotency class class.
NQ manual