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  1. #1
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    Abstract Algebra Help?

    Suppose H and K are subgroups of a group G. If /H/=12 and /K/=35, find /H n K/.



    So far I have this:


    Let a be an element of H and b an element of K, so then a and b are both elements of G. Then I get stuck.

    I am really having trouble with how to work with the orders of H and K in my proof.
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  2. #2
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    Quote Originally Posted by mathwiz2006 View Post
    Suppose H and K are subgroups of a group G. If /H/=12 and /K/=35, find /H n K/.



    So far I have this:


    Let a be an element of H and b an element of K, so then a and b are both elements of G. Then I get stuck.

    I am really having trouble with how to work with the orders of H and K in my proof.

    Hint (elephant size): |HK|=\frac{|H||K|}{|H\cap K|} ...

    Tonio

    Ps. The answer is 420
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  3. #3
    Senior Member Shanks's Avatar
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    the oder of (H intersect K) can't be greater than the oder of H or the oder of K.
    By the Lagerange theorem, the oder of subgroup divides the oder of group.
    thus the order of (H intersect K) is a common divisor of the oder of H and the oder of K. since gcd(12,35)=1, that is, the order of (H intersect K) can only be 1.
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