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GroupTheory

  

ElementOrder

  

compute the order of a group element

  

ElementPower

  

compute  powers of a group element

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

ElementOrder(g, G)

ElementPower(g, n, G)

Parameters

g

-

group element whose order is to be computed

G

-

group containing the element g

n

-

an integer

Description

• 

The order of an element g of a group G is the least positive integer n such that gn is equal to the identity element of G, if one exists, and  otherwise.

• 

The GroupOrder(g, G) command computes the order of the element g of the group G, if possible. Note that this is not always possible in case G is a finitely presented group.

• 

Note that if g is a permutation, then ElementOrder(g, G) is equivalent to PermOrder(g).

• 

The ElementPower( g, n, G ) command computes the power gn of the element g in the group G.

• 

If g is a permutation, then ElementPower( g, n, G ) can be computed more simply as g^n.

Examples

withGroupTheory:

GAlt4

GA4

(1)

ElementOrderPerm1,2,4,G

3

(2)

PermOrderPerm1,2,4

3

(3)

ElementPowerPerm1,2,4,3,G

(4)

ElementPowerPerm1,2,4,2,G

1,4,2

(5)

CCayleyTableGroupG

C < a Cayley table group with 12 elements >

(6)

ElementOrder2&comma;C

2

(7)

ElementOrderElementPower2&comma;3&comma;C&comma;C

2

(8)

Compatibility

• 

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

• 

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

• 

The GroupTheory[ElementPower] command was introduced in Maple 2018.

• 

For more information on Maple 2018 changes, see Updates in Maple 2018.

See Also

GroupTheory[AlternatingGroup]

GroupTheory[CayleyTableGroup]

GroupTheory[Exponent]

GroupTheory[GroupOrder]

GroupTheory