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Math Help - Order of the intersection of groups

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    Order of the intersection of groups

    Suppose H and K are subgroups of a group G. If |H| = 12, |K| = 35. Find |H \cap K|

    My solution:

    By a theorem, I know that |H| and |K| divides |G|, and that the order of every element h in H and k in K divides the order of H and K, respectively. i.e. |h| divides |H| and |k| divides |K|.

    Then the element in |H \cap K| is an element that is commonly shared by both H and K, meaning the elements must have an order that divides both 12 and 35.

    Well, the only number that does that is 1, and the only element with order 1 is the identity. So |H \cap K| = 1.

    Is that right?
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Is that right?
    Yes.
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