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.