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GroupTheory

  

GroupOrder

  

compute the order of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

GroupOrder( G )

Parameters

G

-

a permutation group

Description

• 

The order of a group is the cardinality of its underlying set.

• 

The GroupOrder( G ) command computes the order of the group G, if possible. (Note that the order of a finitely presented group cannot be determined, in general.)

• 

In most cases, it is much more efficient to use the GroupOrder command to determine the order of a group than to list its elements with the Elements command and then count them.  In the case of a symbolic group, this is the only way to compute the group order.

Examples

withGroupTheory:

GSymmetricGroup5

GS5

(1)

GroupOrderG

120

(2)

GBabyMonster

G𝔹

(3)

GroupOrderG

4154781481226426191177580544000000

(4)

GroupOrderDihedralGroup3k+1

6k+2

(5)

GroupOrderElementaryGroupp,n

pn

(6)

Ga,b|a2,b3,a.b5=1

Ga,ba2,b3,ababababab

(7)

GroupOrderG

60

(8)

Compatibility

• 

The GroupTheory[GroupOrder] command was introduced in Maple 17.

• 

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

See Also

GroupTheory

GroupTheory[Elements]

GroupTheory[SymmetricGroup]

 


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