I'm stuck on this problem. Hope someone can give me help.

Let H be a normal subgroup of G, show that if then or

I think I need to construct an isomorphism, but I have no clue how to do it here.

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- Oct 19th 2009, 01:03 AMjackieConjugacy class
I'm stuck on this problem. Hope someone can give me help.

Let H be a normal subgroup of G, show that if then or

I think I need to construct an isomorphism, but I have no clue how to do it here. - Oct 19th 2009, 08:47 AMtonio
- Oct 19th 2009, 09:01 AMjackie
- Oct 19th 2009, 09:31 AMtonio
- Oct 19th 2009, 03:09 PMNonCommAlg
this claim is false! (unless by and you mean something else!) here's a counter-example:

let be a prime number and define and also choose

see that is a normal subgroup of a little work shows that and

however, it can be shown that for any finite group any normal subgroup of and any we have either or - Oct 19th 2009, 08:44 PMjackie
Thank you very much for the help, tonio and NonCommAlg.

You are right NonCommAlg. The question was supposed to include that H is a normal subgroup of index 2 in finite G.

I used the result , similarly . I also used the second isomorphism in my proof.