MHB Group Homomorphism: True or False?

[lemonthree]

Consider the group

.


"The map

defined by

for all

is a group homomorphism."

Is this true or false? I'm guessing it's true because
φ (j) = | j |, which means
φ (j * k) = | j * k |
=| j | * | k |
= φ ( j ) * φ ( k ).

 

[castor28]

Hi lemonthree,

That is true, but you should also check that

• $\phi(x^{-1}) = \phi(x)^{-1}$
• $\phi(1) = 1$