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Math Help - maximal normal subgroup

  1. #1
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    maximal normal subgroup

    Prove that a a normal subgroup  H of the group  G is maximal if and only if the Quotient Group  \frac{G}{H} is simple.
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  2. #2
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    Quote Originally Posted by sashikanth View Post
    Prove that a a normal subgroup  H of the group  G is maximal if and only if the Quotient Group  \frac{G}{H} is simple.

    Remember the correspondence theorem for groups: every subgroup of the quotient group G/H is of the form K/H , where K is a subgroup of G , with the following characteristics:

    1) H < K

    2) [G/H:K/H]=[G:K]

    3) K/H is normal in G/H iff K is normal in G

    Now solve your problem.

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    Remember the correspondence theorem for groups: every subgroup of the quotient group G/H is of the form K/H , where K is a subgroup of G , with the following characteristics:

    1) H < K

    2) [G/H:K/H]=[G:K]

    3) K/H is normal in G/H iff K is normal in G

    Now solve your problem.

    Tonio

    Thanks a lot!
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