I have is a normal subgroup of while is a normal subgroup of .
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 03:13 AM.
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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