Abstract Algebra: Theory and Applications · Problem 11.5.9

Matrix Groups and Symmetry — Thomas Judson

Mathematics — Abstract Algebra · homomorphisms-cyclic-groups

Problem

For

k \in \mathbb{Z}_n

, define a map

\phi_k : \mathbb{Z}_n \to \mathbb{Z}_n

a \mapsto ka

. Prove that

\phi_k

is a homomorphism.