I have found the solution but am having trouble posting it up, mathematical notation in tact. Until I can work out how (or someone tells me) here is the link to it. It is question 2.

http://www.maths.manchester.ac.uk/un...swersheet9.pdf
I think there are two points I need clarifying:

How can we tell from the h.c.f. which primes we need to consider?

If the class number is 2 why does class(B) = class(B^3)? Why does this mean the B is principal? I think these two questions probably result in my limited understanding of the quotient group Ck.

That the class number = 2 means that every fractional ideal (remember?) squared is principal ( hint: if G is a group and K is a normal sbgp. of G of index n, then $\displaystyle g^n\in K\,,\,\,\forall\,g\in G$ ). In our case , $\displaystyle B=B^3\iff B^2=1$ , which is true precisely because the class number is 2...and yes: perhaps you need to dive in a little deeper into that quotient group. Tonio
Thanks for any help, it is greatly appreciated...