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Let F be a field and Aff(F) := {f(x) = ax + b : a, b...

  1. Let F be a field and Aff(F) := {f(x) = ax + b : a, b ∈ F, a ≠ 0} the affine group of F. Prove that Aff(F) is indeed a group under function composition. When is Aff(F) abelian?

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