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Math Help - Finding the number of subgroups

  1. #1
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    Finding the number of subgroups

    Could someone explain to me how to find the number of subgroups in Z_567,000 ?

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  2. #2
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    Jul 2008
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    Exactly the number of divisors of 567,000, which a quick internet search yields The Positive Integer 567000 as the list of such divisors. To see that this is true, let a be a divisor of 567,000. Then the order of a is r=567000/a. Suppose g is another element of order r, so rg = q(567000), thus g=q(567000/r)=q a, so g is in the cyclic subgroup generated by a, thus each divisor corresponds to a unique subgroup of that order.
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