Series involving centres or commutator subgroups are likely to be trivial for abelian groups, but are noted here for completeness.
A composition series for the finite abelian group G returned as a sequence of subgroups.
Given a finite p-group G, return the characteristic subgroup of G generated by the elements xpi, x ∈G, where i is a positive integer.
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.
A descending series of subgroups of G where each quotient is elementary abelian.
The derived series of G.
The upper central series of G.
A subnormal series from G to the subnormal subgroup H.