Subgroup Chains

Series involving centres or commutator subgroups are likely to be trivial for abelian groups, but are noted here for completeness.

ChiefSeries(G) : GrpAb -> [GrpAb]

CompositionSeries(G) : GrpAb -> [GrpAb]

A composition series for the finite abelian group G returned as a sequence of subgroups.

Agemo(G, i) : GrpAb, RngIntElt -> GrpAb

Given a finite p-group G, return the characteristic subgroup of G generated by the elements x^pi, x ∈G, where i is a positive integer.

Omega(G, i) : GrpAb, RngIntElt -> GrpAb

Given a finite p-group G, return the characteristic subgroup of G generated by the elements of order dividing pⁱ, where i is a positive integer.

ElementaryAbelianSeries(G) : GrpAb -> [ GrpAb ]

A descending series of subgroups of G where each quotient is elementary abelian.

DerivedSeries(G) : GrpAb -> [ GrpAb ]

LowerCentralSeries(G) : GrpAb -> [ GrpAb ]

The derived series of G.

UpperCentralSeries(G) : GrpAb -> [ GrpAb ]

The upper central series of G.

SubnormalSeries(G, H) : GrpAb, GrpAb -> [ GrpAb ]

A subnormal series from G to the subnormal subgroup H.