Mathematics 243 – Algebraic Structures Definitions Quiz 9 – November 30, 2012

Your Name:

A) (5) Let a be an element of a group G. Define: the cyclic subgroup of G defined by a, written ⟨a⟩.

B) (5) Let ϕ : (R, +) → (R_{+}, ·) be the mapping defined by ϕ(x) = 7^{x}. Is ϕ a group homomorphism? Why or why not? (Note: R_{+} = {y ∈ R | y > 0}, which is a group under multiplication.)