Question

let G be a group and a,b,belongs to G.then the derived group of G is the subgroup of G generated by elements of some form. find that form.....​

Answer 1

Here is what I've done:

Let xC,yC∈G/C then xyx−1y−1C=C since xyx−1y−1 is a commutator hence belongs to C. But then xyC=yxC so xC and yC commute in G/C. This can be done for any elements, so G/C is abelian.