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In article <1122745589.748359.227100@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"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.
What does one need to know in order to conclude that {G,*} is a group?
Consider. for example, these questions:
Is G closed under * ?
Is * associative?
Is there an identity in {G,*}?
Given such an identity, does each member of G have a multiplicative
inverse in G?
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