GroupTheory
Index
compute the index of a subgroup
Calling Sequence
Parameters
Description
Examples
Compatibility
Index( H, G )
G
-
a group
H
a subgroup of G
The index of a subgroup H of a group G is the number of (left or right) cosets of H in G. If G is finite, then the index of H in G is equal to GH.
The Index( H, G ) command computes the index of the subgroup H of the group G.
withGroupTheory:
IndexAlt4,Alt5
5
G≔a,b|a3=b11
G≔a,b∣a-3b11
H≔Subgroupa·b,a2,G
H≔_G,_G0∣_G-2_G0_G_G0_G-2_G0_G_G0_G-2_G0_G_G0_G-2_G0_G_G0_G-2_G0_G_G0_G-2_G0,_G-2_G0_G-2_G0_G_G0_G-2_G0_G_G0_G-2_G0_G_G0_G-2_G0_G_G0_G-2_G0_G_G0
IndexH,G
2
G≔x,y|y2x=y−2,x2y=x−2:
S≔Subgroupx2,y2,x·y2,G:
IndexS,G
4
The GroupTheory[Index] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
See Also
GroupTheory[AlternatingGroup]
GroupTheory[GroupOrder]
GroupTheory[LeftCosets]
GroupTheory[RightCosets]
GroupTheory[Subgroup]
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