There are only two groups of order 6 (up to isomorphism): and . Since the group in question is abelian, it can't be isomorphic to .
I am trying from two different approached. The first is to try and prove that if |a|=2,3,4,5 then it cannot be in the group for some element a in G.
My other approach was going to be to find an arbitrary order 6 group and then work on the proof from there. I dont seem to know what elements would be in there? G={e, a, b, ab, b^2, ab^2} ?
Thanks in advance.
If he can't use Lagrange then I can't see how can he use that there are only two groups, up to isomorhpism, of order 6...
I suppose that building a Cayley table, using abelian and a try-and-error process will eventually work, but I can't see a straightfroward way to do it without Lagrange.
Tonio