1. Homework Statement
I am translating so bear with me.
We have two group homomorphisms:
α : G → G'
β : G' → G
Let β(α(x)) = x ∀x ∈ G
Show that
1)β is a surjection
2)α an injection
3) ker(β) = ker(α ο β) (Here ο is the composition of functions.)
2. Homework Equations
This is from a...
1. Homework Statement
Are these functions homomorphisms, determine the kernel and image, and identify the quotient group up to isomorphism?
C^∗ is the group of non-zero complex numbers under multiplication, and C is the group of all complex numbers under addition.
2. Homework Equations
φ1 ...