Generator of Dihedral Group
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Theorem
The dihedral group $D_n$ is generated by two elements $\alpha$ and $\beta$ such that:
- $(1): \quad \alpha^n = e$
- $(2): \quad \beta^2 = e$
- $(3): \quad \beta \alpha = \alpha^{n-1} \beta$
Proof
Let $\alpha$ be rotation by $\frac{2 \pi}{n}$.
Let $\beta$ be reflection across the y axis.
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Sources
- Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): $\S 35 \eta$
