Abstract Algebra: Theory and Applications · Problem 11.4.19

Matrix Groups and Symmetry — Thomas Judson

Mathematics — Abstract Algebra · equivalence-relation-homomorphism

Problem

Given a homomorphism

\phi : G \to H

define a relation

\sim

G

a \sim b

\phi(a) = \phi(b)

for

a, b \in G

. Show this relation is an equivalence relation and describe the equivalence classes.