MathDB
Romanian District Olympiad

Source: Grade XII

March 17, 2010
abstract algebragroup theorysuperior algebrasuperior algebra unsolved

Problem Statement

Let G G be a group such that if a,bāˆˆG a,b\in \mathbb{G} and a^2b\equal{}ba^2, then ab\equal{}ba. i)If G G has 2n 2^n elements, prove that G G is abelian. ii) Give an example of a non-abelian group with G G's property from the enounce.
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