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Math Help - 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 e\in C(a) and if x,y\in C(a) then xy\in C(a) and finally if x\in C(a) then 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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