construct the agemo series of a _p_-group
construct the omega series of a _p_-group
AgemoSeries( G )
OmegaSeries( G )
a permutation group
The agemo series of a p-group G, where p is a prime number, is the descending normal series
of G whose terms are the successive agemo subgroups ℧n⁡G of G, where ℧0⁡G=G. See GroupTheory[AgemoPGroup]
The AgemoSeries( G ) command constructs the agemo series of a group G, which must be a finite p-group, for some prime p.
The omega series of a finite p-group G is the ascending normal series
of G, whose terms are the successive omega subgroups Ωn⁡G of G. See GroupTheory[OmegaPGroup].
The OmegaSeries( G ) command constructs the omega series of a finite p-group G.
The group G must be an instance of a permutation group.
Both the agemo and omega series of G are represented by a NormalSeries object which admits certain operations common to all normal series. See GroupTheory[Series].
G ≔ DihedralGroup⁡8
as ≔ AgemoSeries⁡G
os ≔ OmegaSeries⁡G
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