need a help

**dimuk** · August 12th 2008, 08:23 AM

Let H be a subgroup of G then show that $H \capC_G(H)=Z(G)$

**Matt Westwood** · August 12th 2008, 10:50 AM

Can you post that again? It gives "LaTeX Error: Syntax error".

**dimuk** · August 12th 2008, 11:07 AM

Let H be a subgroup of G, then $H\cap C_G(H)=Z(H)$ .

**ThePerfectHacker** · August 12th 2008, 11:43 AM

Originally Posted by dimuk

Let H be a subgroup of G, then $H\cap C_G(H)=Z(H)$ .

Just do it by definition. $Z(H)$ means all $x\in H$ so that $x$ commutes with every element in $G$ . But that is the same thing as $x\in H$ and $x\in C_G(H)$ .

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