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GroupTheory

  

Elements

  

get the elements of an object

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Elements( S )

Parameters

S

-

a group data structure, an orbit, a coset, or conjugacy class

Description

• 

The Elements command computes the set of elements of an object.

• 

The input object S may be a group object, an orbit, a coset, or a conjugacy class.

Examples

withGroupTheory:

GAlt4

GA4

(1)

EElementsG

E1,4,2,1,32,4,1,4,3,1,2,4,1,3,4,2,4,3,1,42,3,1,3,2,1,23,4,,1,2,3,2,3,4

(2)

nopsE=GroupOrderG

12=12

(3)

Check the parity of the elements of G.

mapPermParity,E

1

(4)

orbOrbit2,G

orb2A4

(5)

Elementsorb

1,2,3,4

(6)

HSylowSubgroup2,G

H<a permutation group on 4 letters>

(7)

rcRightCosetsH&comma;G&colon;

crc1

c1&comma;32&comma;4&comma;1&comma;42&comma;3·2&comma;3&comma;4

(8)

Elementsc

1&comma;4&comma;3&comma;1&comma;2&comma;4&comma;1&comma;3&comma;2&comma;2&comma;3&comma;4

(9)

ccConjugacyClassesG

ccA4&comma;1&comma;4&comma;2A4&comma;1&comma;32&comma;4A4&comma;1&comma;4&comma;3A4

(10)

GroupOrderG=addi&comma;i=map`@`nops&comma;Elements&comma;cc

12=12

(11)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[ConjugacyClasses]

GroupTheory[Cosets]

GroupTheory[GroupOrder]

GroupTheory[Orbit]

GroupTheory[PermParity]

GroupTheory[SylowSubgroup]