Proving G/H is Abelian: Normal Subgroups in Abelian Groups

[ehrenfest]

[SOLVED] group theory question

Homework Statement

A student is asked to show that if H is a normal subgroup of an abelian group G, then G/H is abelian. THe student's proof starts as follows:

"We must show that G/H is abelian. Let a and b be two elements of G/H."

Why does the instructor reading this proof expect to find nonsense from here on in the student's paper?

Homework Equations

The Attempt at a Solution

That's probably how I would start my proof...I don't see anything wrong with it.

 

[Mathdope]

Elements of G/H look like Hg, i.e. they are cosets of H in G. Some authors use the notation [g] = Hg to stand for the elements that are "H equivalent" to g.

 

[ehrenfest]

Yeah. I would have then said a must be equal to xH and b must be equal to yH, but I guess it really makes more sense to forget about a and b. Thanks.