Take the tour ×  Given a group $G$ and two conjugated subgroups
$ H $ and $ H'=gHg^{-1} $, is the following proposition true?
There are only two possibilities for the subgroups: either $
H\cap H' = 1 $ or $ H=H'$.  I think that these result it's
false, but I can't find a counterexample (maybe it's true).
Please help me.  share|improve this question What about $D_8$
inside $S_4$? –  user641 Dec 5 '12 at 22:36 Thanks I did it :D!
–  Daniel Dec 5 '12 at 23:15 Some related definitions.
Malnormal: A subgroup $H$ of $G$ is malnormal if $H^g\cap H$ is
trivial for all $g\not\in H$. Cyclonormal: A subgroup $H$ of $G$
is cyclonormal if $H^g\cap H$ is trivial or cyclic for all
$g\not\in H$. Almost-malnormal: A subgroup $H$ of $G$ is almost-
malnormal if $H^g\cap H$ is finite for all $g\not\in H$. Such
subgroups are important in geometric group theory. For example,
malnormal subgroups crop up in the definition of groups with a
quasi-convex hierarchy which were recently used to prove a
(massive!) conjecture of Thurston's.