Abstract Algebra: Theory and Applications · Problem 9.4.6

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · roots-of-unity-isomorphism

Problem

Show that the

n

th roots of unity are isomorphic to

\mathbb{Z}_n

. Hint. Define a map from

\mathbb{Z}_n

into the

n

th roots of unity by

k \mapsto \text{cis}(2k\pi/n)