Access Functions for Groups

The functions described here provide access to basic information stored for a polycyclic group G.

G . i : GrpGPC, RngIntElt -> GrpGPCElt
The i-th polycyclic generator for G if i>0, the inverse of the |i|-th polycyclic generator for G if i<0 and the identity element of G if i=0.
Generators(G) : GrpGPC -> {@ GrpGPCElt @}
PCGenerators(G) : GrpGPC -> {@ GrpGPCElt @}
An indexed set containing the polycyclic generators of G.
Generators(H, G) : GrpGPC, GrpGPC -> {@ GrpGPCElt @}
PCGenerators(H, G) : GrpGPC, GrpGPC -> {@ GrpGPCElt @}
An indexed set containing the polycyclic generators of H as elements of G.
NumberOfGenerators(G) : GrpGPC -> RngIntElt
Ngens(G) : GrpGPC -> RngIntElt
NumberOfPCGenerators(G) : GrpGPC -> RngIntElt
NPCgens(G) : GrpGPC -> RngIntElt
NPCGenerators(G) : GrpGPC -> RngIntElt
The number of polycyclic generators for the polycyclic group G.
PCExponents(G) : GrpGPC -> [RngIntElt]
The orders of the cyclic factors in the polycyclic series defined by the polycyclic presentation of G. The orders are returned in a sequence Q. |Gi/Gi + 1| = mi = Q[i] if Q[i] > 0 and Gi/Gi + 1 is infinite (i.e. i∉I) if Q[i] = 0.
HirschNumber(G) : GrpGPC -> RngIntElt
The Hirsch number of G, i.e. the number of infinite cyclic factors in the polycyclic series defined by the polycyclic presentation of G.

The Hirsch number of G is equal to n - |I|, i.e. to the number of polycyclic generators of G for which there is no power relation. A polycyclic group G is finite if and only if its Hirsch number is 0.

V2.28, 13 July 2023