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
LeftCosets( H, G )
RightCosets( H, G )
G
-
a permutation group or a Cayley table group
H
a subgroup of G
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.
withGroupTheory:
G≔Alt4
G≔A4
GroupOrderG
12
H≔SylowSubgroup2,G
H≔1,23,4,1,32,4
GroupOrderH
4
lc≔LeftCosetsH,G
lc≔·1,23,4,1,32,4,2,3,4·1,23,4,1,32,4,2,4,3·1,23,4,1,32,4
nopslc=GroupOrderGGroupOrderH
3=3
Since the subgroup H is normal in G, the left and right cosets coincide.
mapRepresentative,lc
2,4,3,,2,3,4
mapRepresentative,RightCosetsH,G
IsNormalH,G
true
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[AlternatingGroup]
GroupTheory[Coset]
GroupTheory[GroupOrder]
GroupTheory[IsNormal]
GroupTheory[SylowSubgroup]
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