GroupTheory/AgemoSeries - Maple Help
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GroupTheory

  

AgemoSeries

  

construct the agemo series of a _p_-group

  

OmegaSeries

  

construct the omega series of a _p_-group

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

AgemoSeries( G )

OmegaSeries( G )

Parameters

G

-

a permutation group

Description

• 

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].

Examples

(1)

(2)

(3)

(4)

(5)

See Also

GroupTheory[AgemoPGroup]

GroupTheory[OmegaPGroup]

 


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