I have is a normal subgroup of while is a normal subgroup of . i.e., . Is normal to , i.e., ? why?
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i found a counter example after posting my reply.. but,.. after i got home, alice had posted the counter example i was thinking...
Last edited by kalagota; February 22nd 2009 at 04:13 AM. Reason: error..
Originally Posted by deniselim17 Is normal to , i.e., ? why? A counterexample is, Consider . has a subgroup isomorphic to a Klein-4 group, which is . A normal subgroup of is . However, is not normal in , since .
Here is another counterexample. Consider and and let . We see that but .
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