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GroupTheory

  

LeftCosets

  

construct the left cosets of a subgroup of a group

  

RightCosets

  

construct the right cosets of a subgroup of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

LeftCosets( H, G )

RightCosets( H, G )

Parameters

G

-

a permutation group or a Cayley table group

H

-

a subgroup of G

Description

• 

The LeftCosets( H, G ) command returns the set of left cosets of the subgroup H of the permutation group G.

• 

The RightCosets( H, G ) command returns the set of right cosets of the subgroup H of the permutation group G.

• 

In each case, the collection of cosets (left or right) is returned as a set.

• 

The group G must be an instance of either a permutation group or a Cayley table group, and H must be a subgroup of G.

Examples

withGroupTheory:

GAlt4

GA4

(1)

GroupOrderG

12

(2)

HSylowSubgroup2,G

H<a permutation group on 4 letters>

(3)

GroupOrderH

4

(4)

lcLeftCosetsH&comma;G

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

(5)

nopslc=GroupOrderGGroupOrderH

3=3

(6)

Since the subgroup H is normal in G, the left and right cosets coincide.

mapRepresentative&comma;lc

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

(7)

mapRepresentative&comma;RightCosetsH&comma;G

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

(8)

IsNormalH&comma;G

true

(9)

Compatibility

• 

The GroupTheory[LeftCosets] and GroupTheory[RightCosets] commands were introduced in Maple 17.

• 

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

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[Coset]

GroupTheory[GroupOrder]

GroupTheory[IsNormal]

GroupTheory[SylowSubgroup]