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Math Help - Maximal normal subgroup

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    Maximal normal subgroup

    Prove that H is a normal subgroup of N_{G}(H) and that N_{G}(H) is the largest subgroup of Gcontaining H as a normal subgroup.
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  2. #2
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    Quote Originally Posted by didact273 View Post

    Prove that H is a normal subgroup of N_{G}(H) and that N_{G}(H) is the largest subgroup of G containing H as a normal subgroup.
    very straightforward! just follow the definition of the normalizer of a subgroup.
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    Quote Originally Posted by didact273 View Post
    Prove that H is a normal subgroup of N_{G}(H) and that N_{G}(H) is the largest subgroup of Gcontaining H as a normal subgroup.
    I want to add more to what NonCommAlg said. You need to understand the meaning of "largest". This problem is saying that if K is a subgroup of G so that H is a normal subgroup of K then K\subseteq N(G) i.e. " N(G) is the largest". Show that any element in K must be automatically be an element of N(G) to complete the proof. That is all you need to show, now follow the definition of normalizer.
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