Invariants of an Abelian Group
- ElementaryAbelianQuotient(G, p): GrpAb, RngIntElt -> GrpAb, Map
The maximal \(p\)-elementary abelian quotient of the group \(G\) as
GrpAb. The natural epimorphism is returned as second value.
- FreeAbelianQuotient(G): GrpAb -> GrpAb, Map
The maximal free abelian quotient of the group \(G\) as
GrpAb. The natural epimorphism is returned as second value.
- PrimaryAbelianInvariants(A): GrpAb -> [ RngIntElt ]
- AbelianInvariants(A): GrpAb -> [ RngIntElt ]
The \(p\)-primary invariants of the abelian group \(A\). Each infinite cyclic factor is represented by zero. The non-primary form gives the Smith form invariants, i.e. each element of the sequence divides the next.
- PrimaryAbelianBasis(A): GrpAb -> [ GrpAbElt ], [ RngIntElt ]
- AbelianBasis(A): GrpAb -> [ GrpAbElt ], [ RngIntElt ]
Returns sequences \(B\) and \(I\), where \(I\) are the \(p\)-primary invariants of \(A\), and \(B\) are generators for \(A\) with orders as in \(I\). The non-primary form uses the Smith form invariants, i.e. each element of the sequence divides the next.