Prove or Disprove: Commutator Subgroups

Discussion in 'Undergraduate Math' started by Pedhuts, Nov 29, 2010.

  1. Pedhuts

    Pedhuts Guest

    Prove or disprove that:
    If a*b*(a^-1)*(b^-1)=n
    For all a,b in group (G,*)
    Then the collection of all n, eliminating repetitions, forms a subgroup (C,*)in G.
     
    Pedhuts, Nov 29, 2010
    #1
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  2. So, aside from posting your homework questions in the imperative
    hoping someone will do them for you, and doing so poorly, what else
    are you hoping for?
     
    Arturo Magidin, Nov 30, 2010
    #2
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  3. Pedhuts

    Paul Sperry Guest

    Exercise 3.27 in Rotman's "The Theory of Groups : An Introduction" says
    the following:

    Let G be generated by the elements listed below of the permutation
    group on the letters a, ..., p.

    (ac)(bd);
    (eg)(fh);
    (ik)(jl);
    (mo)(np);
    (ac)(eg)(ik);
    (ab)(cd)(mo);
    (ef)(gh)(mn)(op);
    (ij)(kl).

    Rotman says the commutator subgroup is generated by the first four,
    (ik)(jl)(mo)(np) is in the commutator subgroup but is not a commutator.

    Have fun.
     
    Paul Sperry, Nov 30, 2010
    #3
  4. Help with both writing and technical writing?
     
    William Elliot, Nov 30, 2010
    #4
  5. Pedhuts

    Pedhuts Guest

    Thanks.
     
    Pedhuts, Dec 3, 2010
    #5
  6. Pedhuts

    Pedhuts Guest

    Just hoping that short questions need not long answers, and long questions are not worth asking if you don't learn much from it.

    BTW, bro, it's not a homework question. I ace my math class. So people like me with no competitors in my region get so stuck up that they do stuff outside their curriclum.
     
    Pedhuts, Dec 3, 2010
    #6
  7. Ah; perhaps you are hoping for some remedial work on your grammar?
    Sorry, but I don't have any brothers, dear.
    Just who exactly do you think you are impressing with that bit of
    prose? Assuming without conceding it were true, that is.
     
    Arturo Magidin, Dec 4, 2010
    #7
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