---
tag: 51JC0BDDGH
kind: statement
role: proposition
name: Hajós's theorem
aliases: [minkowskis-lattice-tiling-conjecture, redeis-theorem]
sources:
  - wikipedia: en:12200213@r1356428013
    locator: Hajós's theorem
    note: adopted
    mention: wikipedia://en/12200213
    sections: [Statement]
same_as:
  wikidata: Q1177508
  wikipedia: Hajós's theorem
inventory: [C0EKPAEQ71]
---

## Statement

In 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.