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Math Help - Strutures - groups

  1. #1
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    Strutures - groups

    Hy guys .... I hope that are all fine with you ....

    I had this exercises to do, and I'm having problems to solving them, can some of you,help me?

    **** find the subgroup of the group (Z, +, 0) generated by the set {10, 15} .

    Can you give some link for explanations, or aticles about this area?

    best Regards
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  2. #2
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    Athens, OH, USA
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    Re: Strutures - groups

    Hi,
    You posted this same question three different times. Please don't do this. Post your question only once.

    What is the subgroup generated by {10,15}? It is the intersection of all subgroups that contain both 10 and 15. Let H={10m +15n : m and n are integers}. You can prove H is a subgroup. Furthermore, any subgroup containing both 10 and 15 must contain each element of H. So H is the subgroup generated by 10 and 15. Now the smallest positive integer in H is 5 (5 = (-1)*10 + 1*15) since one characterization of gcd(10,15) is the smallest positive member of H. Finally, then
    H={5n : n is an integer}.
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  3. #3
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    Re: Strutures - groups

    Hi there.... sorry for my wrong behavior, posting the same question in different topics.

    Thank you for advice and you kindly explanation.
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