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Thread: need a help

  1. #1
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    need a help

    Let H be a subgroup of G then show that $\displaystyle H \capC_G(H)=Z(G)$
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  2. #2
    MHF Contributor Matt Westwood's Avatar
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    Can you post that again? It gives "LaTeX Error: Syntax error".
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  3. #3
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    need help

    Let H be a subgroup of G, then $\displaystyle H\cap C_G(H)=Z(H)$.
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  4. #4
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    Quote Originally Posted by dimuk View Post
    Let H be a subgroup of G, then $\displaystyle H\cap C_G(H)=Z(H)$.
    Just do it by definition. $\displaystyle Z(H)$ means all $\displaystyle x\in H$ so that $\displaystyle x$ commutes with every element in $\displaystyle G$. But that is the same thing as $\displaystyle x\in H$ and $\displaystyle x\in C_G(H)$.
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