Mathematics · Abstract Algebra
If G is a group and S is a set, then G acts on S if and only if:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1There is an endomorphism from G to a subgroup H of Sym(S).
- 2There is an automorphism from G to Sym(S), the group of all permutations of S.
- 3There is a homomorphism from G to Sym(S), the group of all permutations of S.✓
- 4There is an isomorphism from G to G.
Correct answer
There is a homomorphism from G to Sym(S), the group of all permutations of S.
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