GroupTheory
AgemoSeries
construct the agemo series of a _p_-group
OmegaSeries
construct the omega series of a _p_-group
Calling Sequence
Parameters
Description
Examples
AgemoSeries( G )
OmegaSeries( G )
G
-
a permutation group
The agemo series of a -group , where is a prime number, is the descending normal series
of whose terms are the successive agemo subgroups of , where . See GroupTheory[AgemoPGroup]
The AgemoSeries( G ) command constructs the agemo series of a group G, which must be a finite -group, for some prime .
The omega series of a finite -group is the ascending normal series
of , whose terms are the successive omega subgroups of . See GroupTheory[OmegaPGroup].
The OmegaSeries( G ) command constructs the omega series of a finite -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].
See Also
GroupTheory[AgemoPGroup]
GroupTheory[OmegaPGroup]
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