Re: Subgroups

In article <43b6b521$0$1051$4fafbaef@xxxxxxxxxxxxxxxxxxx> "Anolethron" <thevery***@xxxxxx> writes:
>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
>
>
What does "intersection of every subgroup of G" mean?
If H is a subgroup of G, do you mean G intersect H
-- this is simply H. Or do you mean the intersection
of _all_ subgroups of G except <e> -- if that interection
has an element f <> e, then perhaps f will be useful
in your construction.

If you allow h = 0, the problem is easy.


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