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Topic: Prove or Disprove: Commutator Subgroups
Replies: 6   Last Post: Dec 3, 2010 9:57 PM

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Paul Sperry

Posts: 1,392
Registered: 12/6/04
Re: Prove or Disprove: Commutator Subgroups
Posted: Nov 29, 2010 11:57 PM
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In article
<669136682.24873.1291071339886.JavaMail.root@gallium.mathforum.org>,
Pedhuts <TSUIM@kernhighmail.com> wrote:

> 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.


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
Columbia, SC (USA)



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