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Math Help - Commutator subgroup of a P-group.

  1. #1
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    Commutator subgroup of a P-group.

    please help me with this sirs/ma'ams, i can't prove it...

    THE COMMUTATOR SUBGROUP OF A FINITE 2-GENERATED P-GROUP OF (NILPOTENCY) CLASS 2 IS CYCLIC

    i'm having difficulties on showing that the commutator subgroup is cyclic, please help me.. thanks
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  2. #2
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    Quote Originally Posted by arvie87 View Post
    please help me with this sirs/ma'ams, i can't prove it...

    THE COMMUTATOR SUBGROUP OF A FINITE 2-GENERATED P-GROUP OF (NILPOTENCY) CLASS 2 IS CYCLIC

    i'm having difficulties on showing that the commutator subgroup is cyclic, please help me.. thanks

    This is theorem 5.2.18 in Robinson's "A Course in the Theory of Groups" (2nd ed. 1996, page 137) .

    Tonio
    Last edited by mr fantastic; July 1st 2010 at 03:28 PM.
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  3. #3
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    order of the commutator subgroup

    maybe someone know the following theorem and knows how to prove or any book, where I can find it:

    Let G be a p-group. The indices of centralizers are bounded by p for every x in G. Then, the order of the commutator subgroup is bounded by p:
    |G| = p^n, |G:C_G(x)| <= p for all x in G => |G'| <= p
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  4. #4
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    Quote Originally Posted by nelig100 View Post
    maybe someone know the following theorem and knows how to prove or any book, where I can find it:

    Let G be a p-group. The indices of centralizers are bounded by p for every x in G. Then, the order of the commutator subgroup is bounded by p:
    |G| = p^n, |G:C_G(x)| <= p for all x in G => |G'| <= p

    Do not "kidnap" other poster's thread: begin a new one with your question in it.

    Tonio
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