Hello,(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question on conjugate closure of subgroups

**Physics Forums | Science Articles, Homework Help, Discussion**