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Topic: How to show that if a group G has finitely many subgroups, then G is finite?
Replies: 5   Last Post: Nov 24, 2005 12:00 PM

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Bijan Mobasseri

Posts: 18
Registered: 12/7/04
Re: How to show that if a group G has finitely many subgroups, then G is finite?
Posted: Nov 23, 2005 12:00 PM
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In article <dlvatc$4r6$1@dizzy.math.ohio-state.edu>, nymphcc@hotmail.com wrote:

> How to show that if G has finitely many subgroups, then G is finite?

If G has element g of infinite order then <g> has infinitely many sbgs.
So all elements have finite order. So finite number of them. Done.




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