Answer to Question #121071 in Abstract Algebra for Samson

Question

Let
G
1
G1 and
G
2
G2 be two groups and
f
:
G
1

i
g
h
t
a
r
r
o
w
G
2
f:G1 ightarrowG2 be a homomorphism, then the kernel of f is define by

Answer 1

$\ker f=\{x\in G_1: f(x)=I_{G_2}\}$, where $I_{G_2}$ is the identity element of $G_2$.