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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
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.


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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