Mathematics · Abstract Algebra
Let G = R − {0} and H = {-1, 1} be groups under multiplication. Then, the map φ : G → H defined by φ(x) = x / |x| is:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Not a homomorphism
- 2A one-to-one (injective) homomorphism, which is not onto
- 3An onto (surjective) homomorphism, which is not one-to-one✓
- 4An isomorphism
Correct answer
An onto (surjective) homomorphism, which is not one-to-one
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