(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that an abelian group with two elements of order 2 must have a subgroup of order 4

2. Relevant equations

3. The attempt at a solution

Let G be an abelian group ==> for every a,b that belong to G ab=ba.

Let a,b have order 2 ==> a^2 =e and b^2 = e. Since a belongs to G aa=a^2 belongs to G. Since b belongs to G bb= b^2 belongs to G. IE four elements ie order of a subgroup can be four.

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# Homework Help: Abelian Groups

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