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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




Re: How to show that if a group G has finitely many subgroups, then G is finite?
Posted:
Nov 23, 2005 12:00 PM


In article <dlvatc$4r6$1@dizzy.math.ohiostate.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.



