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Romania District MO 2022 Grade 12 P2

Source: Romania District MO 2022 Grade 12

March 27, 2022
group theoryabelian groupromaniacollege contests

Problem Statement

Let (G,⋅)(G,\cdot) be a group and H≠GH\neq G be a subgroup so that x2=y2x^2=y^2 for all x,y∈G∖H.x,y\in G\setminus H. Show that (H,⋅)(H,\cdot) is an Abelian group.
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