Definition:Multiplicative Group of Complex Roots of Unity

Definition

Let $n \in \Z$ be an integer such that $n > 0$.

Let $U_n := \set {z \in \C: z^n = 1}$ denote the set of complex $n$th roots of unity.

Let $\struct {U_n, \times}$ be the algebraic structure formed by $U_n$ under complex multiplication.

Then $\struct {U_n, \times}$ is the multiplicative group of complex $n$th roots of unity.

Also denoted as

Some sources denote this group as $K_n$.

Also see

• Roots of Unity under Multiplication form Cyclic Group

Sources

• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $4$: Subgroups: Example $4.8$