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Math Help - generator for groups.

  1. #1
    Junior Member
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    generator for groups.

    G=(Z,+)
    X ={2,3}

    Does X generate G???

    My answer is no because X will only generate the set 2Z and 3Z but not Z...
    Is this right if this is wrong please explain why???
    Last edited by mr fantastic; October 29th 2010 at 04:50 AM. Reason: Edited title.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Dreamer78692 View Post
    G=(Z,+)
    X ={2,3}

    Does X generate G???

    My answer is no because X will only generate the set 2Z and 3Z but not Z...
    Is this right if this is wrong please explain why???
    No, that's not right. For example, 2+2+3=7 \not\in 2 \mathbb{Z} \cup 3 \mathbb{Z}.

    What you need to do for this question is to apply the Euclidean algorithm. 2 and 3 are coprime, so...
    Last edited by Swlabr; October 29th 2010 at 12:32 AM.
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