Mathematics · Group Theory
Let G be a finite group. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If for every positive integer m dividing |G|, G has a subgroup of order m, then G is abelian.
- 2If G is cyclic, then for any two subgroups A and B of G, either A ⊂ B or B ⊂ A.
- 3If for any two subgroups A and B of G, either A ⊂ B or B ⊂ A, then G is cyclic.
- 4If g ∈ G has order m and if n ≥ 1 divides m, then G has a subgroup of order n.✓
Correct answer
If g ∈ G has order m and if n ≥ 1 divides m, then G has a subgroup of order n.
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