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This is quite old, but since it is not answered:
One way to do this is do use the (built-in) version of GAP to test the conjugacy.
This has the function RepresentativeAction(g,g1,g2) which takes three arguments, g, g1, g2 and either returns fail if g1 and g2 are not conjugate in g, or returns a conjugating element if they are.
You need to turn everything into a GAP-object in order to do this.
gap.RepresentativeAction(gap("SymmetricGroup(3)"), gap(G1), gap(G2))
This returns () which is the identity, indicating that the groups are not only conjugate, but identical.
| | 2 | No.2 Revision |
This is quite old, but since it is not answered:
One way to do this is do use the (built-in) version of GAP to test the conjugacy.
This has the function RepresentativeAction(g,g1,g2) which takes three arguments, g, g1, g2 and either returns fail if g1 and g2 are not conjugate in g, or returns a conjugating element if they are.
You need to turn everything into a GAP-object in order to do this.
gap.RepresentativeAction(gap("SymmetricGroup(3)"), gap(G1), gap(G2))
This returns () which is the identity, indicating that the groups are not only conjugate, but identical.
EDIT: if you define
S = SymmetricGroup(3)
gen1 = Permutation('(1,2)(3)')
gen2 = Permutation('(1,3)(2)')
H1=S.subgroup([gen1])
H2=S.subgroup([gen2])
You'll see that you get
sage: gap.RepresentativeAction(gap(S),gap(H1),gap(H2))
(2,3)
so the subgroups are conjugate, but not identical. Useful to know how to get this info, though!
