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Math Help - AxB

  1. #1
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    AxB

    Let A, B be groups. Prove that the following sets are subgroups of AxB:

    \{a\times e:a\in A\}

    Not sure how to do this with ordered pairs.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: AxB

    Quote Originally Posted by dwsmith View Post
    Let A, B be groups. Prove that the following sets are subgroups of AxB:

    \{a\times e:a\in A\}

    Not sure how to do this with ordered pairs.
    Well, you can do it directly, but let me ask you this. The projection \pi:A\times B\to A:      (a,b)\mapsto a is a homomorphism by definition, right? What is its kernel?
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