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GroupTheory

  

Index

  

compute the index of a subgroup

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Index( H, G )

Parameters

G

-

a group

H

-

a subgroup of G

Description

• 

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.

Examples

withGroupTheory:

IndexAlt4,Alt5

5

(1)

Ga,b|a3=b11

Ga,ba-3b11

(2)

HSubgroupa·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

(3)

IndexH,G

2

(4)

Gx,y|y2x=y2,x2y=x2:

SSubgroupx2,y2,x·y2,G:

IndexS,G

4

(5)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[GroupOrder]

GroupTheory[LeftCosets]

GroupTheory[RightCosets]

GroupTheory[Subgroup]