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On 30 Jul 2005 10:46:29 -0700, "ADH" <adoug48@xxxxxxxxxxx> wrote:
>Hi,
>I'm trying to solve this problem on group theory. Most of the problems
>I was able to handle were Zn and U(n) (integers under addition and
>multiplication) but now I'm faced with rationals. I have no idea where
>to start.
>Problem: Let G= {a+b*sqrt(2)},where a and b are rational numbers not
>both 0. Prove that G is a group under ordinary multiplication.
Verify the axioms for a group.
Is G closed under multiplication? If it's not obvious, try a few test
cases by actually choosing 2 elements of G and then multiplying them
out algebraically.
Does G have a multiplicative identity?
Associativity is automatic for G. Why?
What about inverses? It's easy to see that each element of G has a
multiplicative inverse in the reals, but you need to show that the
inverse is an element of G.
Try to work these out, one at a time.
quasi
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