Mathematics · Group Theory
Let G be a group. Which of the following maps is NOT a group action?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1G × G → G given by g.a = gag-1 for all g ∈ G and a ∈ G.
- 2G × H → H given by g.h = ghg-1 for all g ∈ G and h ∈ H, where H is a normal subgroup of G.
- 3G × G → G given by g.a = ga for all g ∈ G and a ∈ G.
- 4G × H → H given by g.h = ghg-1 for all g ∈ G and h ∈ H, where H is a subset of G.✓
Correct answer
G × H → H given by g.h = ghg-1 for all g ∈ G and h ∈ H, where H is a subset of G.
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