# A question about the commutator subgroup

Submitted by Mike G on Thu, 09/02/2004 - 08:43.

We all know that commutators can be used to generate half of the Cube group G. My first question is: Can all elements of the commutator subgroup themselves be written as commutators? i.e., the problem is to determine whether the set of commutators is closed under multiplication; it need not be in general, but is it true here?

If it is closed in this case, then a natural question to ask is How do we write a given element of the commutator subgroup as a single commutator?

On the other hand, if the set of commutators is NOT closed under multiplication, then how many elements of G can be written in commutator form?

I'm sorry if there was a discusssion of these or similar questions in the old Cube Lovers forum, but I could not find it in the archive.

If it is closed in this case, then a natural question to ask is How do we write a given element of the commutator subgroup as a single commutator?

On the other hand, if the set of commutators is NOT closed under multiplication, then how many elements of G can be written in commutator form?

I'm sorry if there was a discusssion of these or similar questions in the old Cube Lovers forum, but I could not find it in the archive.