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Math Help - Quotient group

  1. #1
    Junior Member hercules's Avatar
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    Quotient group

    Please help me with the following proof....my mind doesn't seem to be working right now.

    Assume N is a normal subgroup of G.
    a) Prove that if [G:N] is a prime, then G/N is cyclic. (could you provide an example as well)
    b) Prove or disprove the converse of the statement in part (a).

    Thank You.
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  2. #2
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    Quote Originally Posted by hercules View Post
    Please help me with the following proof....my mind doesn't seem to be working right now.

    Assume N is a normal subgroup of G.
    a) Prove that if [G:N] is a prime, then G/N is cyclic. (could you provide an example as well)
    b) Prove or disprove the converse of the statement in part (a).
    a)If G is a finite group then |G/N| = [G:N]. Prime groups are cyclic, so G/N is cyclic.
    b)It is false. Try something.
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  3. #3
    Junior Member hercules's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    a)If G is a finite group then |G/N| = [G:N]. Prime groups are cyclic, so G/N is cyclic.
    b)It is false. Try something.

    wow....lightening quick response ...thank you.
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  4. #4
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    Quote Originally Posted by hercules View Post
    wow....lightening quick response ...thank you.
    I am the fastest responder in the West.

    Also, why would this Forum claim to be the fastest responding forum on the internet if it was not true?
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