Subgroups

Let G be a group such that the intersection of every subgroup of G except
<e> is a subgroup that is different from <e>. Show that for every element g
belonging to G there is an integer h such that g^h=e

(e is the neutral element for the operation of G).


Now: how do I show that?I mean especially if the intersection is not finite
(which might happen I guess, and I find hard...)?

Thanks in advance


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