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 Quote by jbunniii This is not true in general. If xH and yK are not subgroups, then neither contains the identity, so their intersection also doesn't contain the identiy. So it can't be a subgroup. Moreover, in general $xH \cap yK$ isn't even a subSET of H or K. xH and H are disjoint unless $x \in H$. Similarly for yK and K.
Sorry, I made some mistakes when I wrote the post. In fact, I mean the intersection of H and K is a subgroup of both H and K...Could U give me some tips to prove it?