# Prove or Disprove: Commutator Subgroups

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

1. ### PedhutsGuest

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

2. ### Arturo MagidinGuest

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

3. ### Paul SperryGuest

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
4. ### William ElliotGuest

Help with both writing and technical writing?

William Elliot, Nov 30, 2010
5. ### PedhutsGuest

Thanks.

Pedhuts, Dec 3, 2010
6. ### PedhutsGuest

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
7. ### Arturo MagidinGuest

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