# need a help

• August 12th 2008, 09:23 AM
dimuk
need a help
Let H be a subgroup of G then show that $H \capC_G(H)=Z(G)$
• August 12th 2008, 11:50 AM
Matt Westwood
Can you post that again? It gives "LaTeX Error: Syntax error".
• August 12th 2008, 12:07 PM
dimuk
need help
Let H be a subgroup of G, then $H\cap C_G(H)=Z(H)$.
• August 12th 2008, 12:43 PM
ThePerfectHacker
Quote:

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 $x\in C_G(H)$.