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Feb28-12, 05:26 PM
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 [itex]xH \cap yK[/itex] isn't even a subSET of H or K. xH and H are disjoint unless [itex]x \in H[/itex]. 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?