# Subgroups..

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• Jul 6th 2008, 11:54 AM
Vedicmaths
Subgroups..
I need help in another subgroup problem...
please help!

--->Assume that G is a subgroup with operation * and that a E G. Let..
C(a) = { x E G : a *x = x*a}.
prove that C(a) is a subgroup of G?

using the property..
Let G be a group with operation * and let H be a subset of G. Then H is a subgroup of G if and only if:
1) H is non empty.

2) If a E H and b E H then a*b E H

3) If a E H then a(inverse) E H.
• Jul 6th 2008, 12:03 PM
ThePerfectHacker
Quote:

Originally Posted by Vedicmaths
--->Assume that G is a subgroup with operation * and that a E G. Let..
C(a) = { x E G : a *x = x*a}.
prove that C(a) is a subgroup of G?

Just do this by definition, that is the easiet way to do this. You need to show $\displaystyle e\in C(a)$ and if $\displaystyle x,y\in C(a)$ then $\displaystyle xy\in C(a)$ and finally if $\displaystyle x\in C(a)$ then $\displaystyle x^{-1} \in C(a)$.
• Jul 6th 2008, 07:51 PM
Vedicmaths
Thanks a lot!

yeah I was making it too completed...it was similar to the last one!