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Thread: Subgroups..

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by Vedicmaths View Post
    --->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 $\displaystyle x^{-1} \in C(a)$.
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  3. #3
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    Thanks a lot!

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