Abstract Algebra: Theory and Applications · Problem 11.4.9

Matrix Groups and Symmetry — Thomas Judson

Mathematics — Abstract Algebra · homomorphic-image-abelian

Problem

\phi : G \to H

is a group homomorphism and

G

is abelian, prove that

\phi(G)

is also abelian. Hint. Let

a, b \in G

. Then

\phi(a)\phi(b) = \phi(ab) = \phi(ba) = \phi(b)\phi(a)