Abstract Algebra: Theory and Applications · Problem 11.4.15

Matrix Groups and Symmetry — Thomas Judson

Mathematics — Abstract Algebra · induced-homomorphism-quotient-groups

Problem

Let

G_1

and

G_2

be groups, and let

H_1

and

H_2

be normal subgroups of

G_1

and

G_2

respectively. Let

\phi : G_1 \to G_2

be a homomorphism. Show that

\phi

induces a homomorphism

\bar{\phi} : (G_1/H_1) \to (G_2/H_2)

\phi(H_1) \subset H_2