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 $G_2$.