Mathematics · Group Theory
Let G be a group. For g ∈ G, define πg : G → G by πg(h) = gh, ∀ h ∈ G. For v ∈ &mathbb{R}n, define Tv : &mathbb{R}n → &mathbb{R}n by Tv(w) = v + w, ∀ w ∈ &mathbb{R}n. Which of the following statements is true regarding group actions?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Tv defines a group action but πg does not.
- 2Both Tv (of the additive group &mathbb{R}n on &mathbb{R}n) and πg (of G on G) define group actions.✓
- 3πg defines a group action but Tv does not.
- 4Neither Tv nor πg defines a group action.
Correct answer
Both Tv (of the additive group &mathbb{R}n on &mathbb{R}n) and πg (of G on G) define group actions.
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