The complex roots of unity form a multiplicative group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.8 Let $G = \{ z \in \mathbb{C} \ |\ z^n = 1 \mathrm{for\ some} n \in…
The reals mod the integers are an abelian group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.7 Let $G = \{ x \in \mathbb{R} \ |\ 0 \leq x < 1 \}$ and…