construct the lower p-central series of a group
LowerPCentralSeries( p, G )
a prime number
a permutation group
The lower p-central series of a group G, for a prime number p, is the descending normal series of G whose terms are the successive subgroups, defined as follows. Let G0=G and, for 0<k, define Gk=Gp·G,Gk−1. The sequence
is called the lower p-central series of G. If the p-residual Gc is the trivial group, then G is a p-group. In this case, the number c is called the p- class of G.
The LowerPCentralSeries( G ) command constructs the lower p-central series of a group G.
The group G must be an instance of a permutation group.
The lower p-central series of G is represented by a series data structure which admits certain operations common to all series. See GroupTheory[Series].
G ≔ PermutationGroup⁡Perm⁡1,2,Perm⁡1,2,3,4,5
The GroupTheory[LowerPCentralSeries] command was introduced in Maple 2019.
For more information on Maple 2019 changes, see Updates in Maple 2019.
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