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GroupTheory

  

Generators

  

obtain the generators of a group

  

NonRedundantGenerators

  

obtain the generators of a group, with redundant ones filtered out

  

Labels

  

obtain labels for the generators of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Generators(g)

NonRedundantGenerators(g)

Labels(g)

Parameters

g

-

group data structure

Description

• 

The Generators command returns a list of generators of a group.

• 

The NonRedundantGenerators command returns a list of generators of a group, with redundant generators removed (no proper subset of the generators will generate the full group). This is typically a bit more time-consuming to compute than Generators.

• 

The Labels command returns a list of labels for the generators of a group, or undefined if no labels are defined. In the first case, the labels are in the same order as the list that Generators returns.

Examples

withGroupTheory:

g1Groupa=Perm1,2,b=Perm2,3,Perm3,4

g11,2,2,3,3,4

(1)

Generatorsg1

1,2,2,3,3,4

(2)

Maple selects a label for the generator missing one.

Labelsg1

a,b,_G

(3)

In this case, none of the generators are labeled, so Maple does not select any labels.

g2Group1,2,2,3,3,4

g21,2,2,3,3,4

(4)

Labelsg2

undefined

(5)

Finitely presented groups use the names of the generators as labels.

g3Groupa,b,a,a,b,b,a,b,a,b

g3a,ba2,b2,abab

(6)

Labelsg3

a,b

(7)

A Cayley table groups returns all its elements as its list of generators.

g4Group1|2|3,2|3|1,3|1|2

g4 < a Cayley table group with 3 elements >

(8)

Generatorsg4

1&comma;2&comma;3

(9)

NonRedundantGeneratorsg4

2

(10)

Compatibility

• 

The GroupTheory[Generators], GroupTheory[NonRedundantGenerators] and GroupTheory[Labels] commands were introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

GroupTheory

GroupTheory[Group]