11 | Fundamental Theorem of Finite Abelian Groups 22111. Prove that every finite Abelian group can be expressed as the(external) direct product of cyclic groups of orders n₁, n₂,..., nowhere n+1divides n, for i = 1, 2, . . . , t —- 1. (This exercise is re-ferred to in this chapter.)

Fundamental Theorem of Finite Abelian Groups: Every finite Abelian group is a direct product of…

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Elements Of Modern Algebra

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Author:Gilbert, Linda, Jimmie

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Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 23E: Prove that if r and s are relatively prime positive integers, then any cyclic group of order rs is...

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Prove that every finite Abelian group can be expressed as the (external) direct product of cyclic groups of orders n₁, ₂, ..., n where n₁+1 divides n, for i for i = 1, 2, ..., t - 1. (This exercise is re- ferred to in this chapter.)