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Math Help - Exam study guide help

  1. #1
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    Exam study guide help

    This is of my final study guide, and Im confused by the question please help....

    For H,K \leq G Set H~ K when for some g \in G, K = g^{-1} Hg


    Finish the Statement: "|[ H]_~| = 1 \iff H is...." and justify your answer

    Thanks in advance...
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by ElieWiesel View Post
    This is of my final study guide, and Im confused by the question please help....

    For H,K \leq G Set H~ K when for some g \in G, K = g^{-1} Hg


    Finish the Statement: "|[ H]_~| = 1 \iff H is...." and justify your answer

    Thanks in advance...
    What does \left|\left[H\right]_\sim\right| mean?
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  3. #3
    Senior Member Shanks's Avatar
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    \left|\left[H\right]_\sim\right|=1\iff \text{ for all } g\in G, H=g^{-1}Hg \iff H\text{ is normal subgroup of }G
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