# Abstract Algebra : Abelian Groups, Cauchy's Theorem, LaGrange's Theorem and Sylow Subgroups

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Let G be a nonabelian group of order 6. Show carefully that G must contain three elements of period 2 and two elements of period 3.

Let G be an abelian group of order 2n where n is odd. Determine how many elements of period 2 are contained in G. Fact: G must contain at least one element of period 2 (assume).

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#### Solution Summary

Abelian Groups, Cauchy's Theorem, LaGrange's Theorem and Sylow Subgroups are investigated.

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