test conjugacy of elements of a permutation group
compute the conjugator of elements of a permutation group
AreConjugate( a, b, G )
Conjugator( a, b, G )
a permutation group
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.
G ≔ PermutationGroup⁡Perm⁡2,4,6,Perm⁡1,5,2,4,Perm⁡1,4,2,5,3,6
a ≔ Perm⁡1,2,3,4,5,6
b ≔ Perm⁡1,2,3,6,4,5
c ≔ Perm⁡1,4,2,5,3,6
d ≔ Conjugator⁡a,c,G
The GroupTheory[AreConjugate] and GroupTheory[Conjugator] commands were introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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