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GroupTheory

  

AreConjugate

  

test conjugacy of elements of a permutation group

  

Conjugator

  

compute the conjugator of elements of a permutation group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

AreConjugate( a, b, G )

Conjugator( a, b, G )

Parameters

G

-

a permutation group

a

-

permutation

b

-

permutation

Description

• 

Two elements a and b of a group G are conjugate in G if there is an element g in G such that g-1·a·g=b . Any such element g is called a conjugator.  A conjugator is not generally uniquely determined by a and b.

• 

The AreConjugate( a, b, G ) command returns true if the permutations a and b are conjugate in the permutation group G, and returns false otherwise.

• 

The Conjugator( a, b, G ) command returns an element g in G such that g^(-1) . a . g = b, provided that a and b are conjugate in G. If a and b are not conjugate in G, the value FAIL is returned.

• 

The group G must be an instance of a permutation group, and the permutations a and b must be members of G.

Examples

withGroupTheory:

GPermutationGroupPerm2,4,6,Perm1,5,2,4,Perm1,4,2,5,3,6

G2,4,6,1,52,4,1,42,53,6

(1)

aPerm1,2,3,4,5,6

a1,23,45,6

(2)

bPerm1,2,3,6,4,5

b1,23,64,5

(3)

AreConjugatea,b,G

false

(4)

AreConjugatea,b,Symm6

true

(5)

cPerm1,4,2,5,3,6

c1,42,53,6

(6)

AreConjugatea,c,G

true

(7)

dConjugatora,c,G

d2,4,6

(8)

d1·a·d=c

1,42,53,6=1,42,53,6

(9)

Compatibility

• 

The GroupTheory[AreConjugate] and GroupTheory[Conjugator] commands were introduced in Maple 17.

• 

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

See Also

GroupTheory

GroupTheory[ConjugacyClass]