Condition for Linear Operation on Complex Numbers to be of Finite Order
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This theorem requires a proof.
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Theorem
Let $A$ be the operation on the complex numbers $\C$ defined as:
- $\map A x = \alpha x + \beta$
Then $A$ is of finite order greater than $1$ if and only if $\alpha$ is a root of unity other than $1$.
Proof
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Sources
- 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: Examples: $(3)$
