hello everyone. Can any one help me on this: H and K are subgroups of G, K is also normal in G. I want to find a counterexample that HK is not normal in G. Thanks!!
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Originally Posted by xxie hello everyone. Can any one help me on this: H and K are subgroups of G, K is also normal in G. I want to find a counterexample that HK is not normal in G. Thanks!! and the Klein four group.
what is K=V????
Originally Posted by xxie what is K=V???? i mentioned that, didn't i? it's the Klein four group:
oh~thanks! i didn't know what klein group is!haha
Originally Posted by xxie hello everyone. Can any one help me on this: H and K are subgroups of G, K is also normal in G. I want to find a counterexample that HK is not normal in G. Thanks!! Hi xxie. Here is a much simpler example. Take
Last edited by TheAbstractionist; May 7th 2009 at 04:46 AM.
Originally Posted by TheAbstractionist Hi xxie. Here is a much simpler example. Take allowing K = (1) will make the problem trivial and non-interesting, isn't it?
Originally Posted by NonCommAlg allowing K = (1) will make the problem trivial and non-interesting, isn't it? Hi NonCommAlg. As xxie didn’t state any condition on what type of normal subgroup should be, my example was a fair one. But, if you like, how about
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