Let $S$ be the set $\{a + b\sqrt{2}|a,b \in \mathbb{Q}$. Please show

• that $S$ is a group under addition. We will denote this group $(S,+)$.
• and that $(S,+)$ is abelian
• that $S-{0}$ is a group under multiplication. We will denote this group as $(S-{0},*)$.

• There are more properties, I will add them later. I'm going to add all the properties of a field.

problem.a_b_sqrt_2.tex

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\begin{problem}
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• Dihedral group

problem