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  "body": "\n## Statement\n\nIn group theory, **Hajós's theorem** states that if a finite abelian group is expressed as the [[Cartesian product|09CEDJYBKP]] of simplexes, that is, sets of the form $\\{e,a,a^2,\\dots,a^{s-1}\\}$ where $e$ is the [[identity element|07WYQPB8E3]], then at least one of the factors is a [[subgroup|0X1JXT47GA]]. The theorem was [[proved|0B94TKFQJX]] by the Hungarian mathematician György Hajós in 1941 using group rings. Rédei later proved the statement when the factors are only required to contain the identity element and be of prime [[cardinality|0G0ASKNA6Z]]. Rédei's proof of Hajós's theorem was simplified by Tibor Szele.\n",
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