# What is the center of $V$, the Klein 4 group?

Please help - in my notes, it is the group $V$ itself. I just want to confirm this. Can you also explain and give an example if that is possible?

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Every abelian group is its own center. If you look at the definitions you will see this.

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alright!! thanks! :)) – gggg Sep 30 '10 at 20:04

You know, this group has only 4 elements. You could just multiply them out. Really, there are only three worthwhile elements, as one is an identity and that commutes with everything.

It would take less than 5 minutes, and you could do it Cayley style or full-on multiplication table style. It would probably even be good for you, as you might get a feel for what groups really are.

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You're answering to a thread more than a year old. I hope OP has figured it out by now :) – t.b. Dec 13 '11 at 9:48
Besides - Cayley graphs don't make you feel what groups really are. – Martin Brandenburg Dec 13 '11 at 10:20
@t.b. Oh... Zev edited the question 14 hours ago, and I never pay attention to original post dates. So I thought I was answering an hour-old thread. Whoops. – mixedmath Dec 13 '11 at 22:46
@Martin: I never said cayley graphs would make him get a good feel, I said carrying out the multiplication would. I think this problem demonstrated a lack of understanding of group computation, that's all. – mixedmath Dec 13 '11 at 22:47