Definition:Circle Group
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Definition
Let $K$ be the set of all complex numbers of unit modulus:
- $K = \set {z \in \C: \cmod z = 1}$
Consider the algebraic structure $\struct {K, \times}$ where $\times$ denotes the operation of complex multiplication.
Then $\struct {K, \times}$ is called the circle group.
Also known as
It is also seen with the fuller title the complex unit circle (group).
Also see
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 12$: Homomorphisms: Example $12.1$
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Examples of Group Structure: $\S 31$