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19 Nov 2019
. Let G be a fnite abelian group, and let d be a divisor of GI. Prove that there is a subgroup of G of order d. Hint: Use the fundamental theorem of finite abelian groups and the previous exercise. This is a converse of Lagrange's theorem for finite abelian groups.) . Suppose that G is a finite abelian group that has exactly one subgroup for each divisor of (GI. Prove that G is cyclic.
. Let G be a fnite abelian group, and let d be a divisor of GI. Prove that there is a subgroup of G of order d. Hint: Use the fundamental theorem of finite abelian groups and the previous exercise. This is a converse of Lagrange's theorem for finite abelian groups.) . Suppose that G is a finite abelian group that has exactly one subgroup for each divisor of (GI. Prove that G is cyclic.
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Lelia LubowitzLv2
4 Jul 2019
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