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Let's have a groupGand two subgroupsA<GandB<Gsuch that the intersection of A and B is trivial.

I consider the subgroup [itex]\left\langle A^B \right\rangle[/itex] which is calledconjugate closureofAwith respect toB, and it is the subgroup generated by the set: [tex]A^B=\{ b^{-1}ab \;|\; a\in A,\; b\in B\}[/tex]

It is clear that [itex]A\cap \left\langle A^B \right\rangle = A[/itex].

What about [itex]B\cap \left\langle A^B \right\rangle[/itex]?

DoBand the conjugate closure [itex]\left\langle A^B \right\rangle[/itex] have trivial intersection?

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# Question on conjugate closure of subgroups

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