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GroupTheory

  

Exponent

  

compute the exponent of a finite group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Exponent(G)

Parameters

G

-

a permutation group or a Cayley table group

Description

• 

The exponent of a finite group G is the least positive integer e such that g^e = 1, for all g in G. It is equal to the least common multiple of the orders of the elements of G, and is a divisor of the order of G.

• 

The Exponent(G) command computes the exponent of the finite group G, if possible.

• 

Note that the exponent of a finite finitely presented group can be computed by first converting it to a permutation group using the PermutationGroup command.

Examples

withGroupTheory:

GSymmetricGroup5

GS5

(1)

ExponentG

60

(2)

ExponentElementaryGroup7,3

7

(3)

Ga,b|a2,b3,a·b5=1

Ga,ba2,b3,ababababab

(4)

ExponentG

Error, (in Exponent) cannot compute the exponent of a general finitely presented group.  If you know that your group is finite, try converting it to a permutation group by using the `PermutationGroup' command with your finitely presented group as input.

ExponentPermutationGroupG

30

(5)

Compatibility

• 

The GroupTheory[Exponent] command was introduced in Maple 2015.

• 

For more information on Maple 2015 changes, see Updates in Maple 2015.

See Also

GroupTheory

GroupTheory[ElementaryGroup]

GroupTheory[GroupOrder]

GroupTheory[PermutationGroup]

GroupTheory[SymmetricGroup]

with