1. A

    Show injectivity, surjectivity and kernel of groups

    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...
  2. T

    I Images of elements in a group homomorphism

    Why does the image of elements in a homomorphism depend on the image of 1? Why not the other generators?
  3. U

    Are these homomorphisms?

    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 ...