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later proved the statement when the factors are only required to contain the identity element and be of prime cardinality. Rédei's proof of Hajós's theorem was simplified by
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351:; Szabó, Sándor (1994), "The group theoretic version of Minkowski's conjecture; more about the algebraic version of Minkowski s conjecture",
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In this lattice tiling of the plane by congruent squares, the green and violet squares meet edge-to-edge as do the blue and orange squares.
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269:(1965), "Die neue Theorie der endlichen abelschen Gruppen und Verallgemeinerung des Hauptsatzes von Hajós",
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is the same conjecture for non-lattice tilings, which turns out to be false in high dimensions.
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An equivalent statement on homogeneous linear forms was originally conjectured by
386:(1949), "Neuer vereinfachter Beweis des gruppentheoretischen Satzes von Hajós",
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is the identity element, then at least one of the factors is a
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Algebra and Tiling: Homomorphisms in the
Service of Geometry
130:. The theorem was proved by the Hungarian mathematician
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161:. A consequence is Minkowski's conjecture on lattice
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182:(1941), "Über einfache und mehrfache Bedeckung des
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272:Acta Mathematica Academiae Scientiarum Hungaricae
357:, Carus Mathematical Monographs, vol. 25,
202:-dimensionalen Raumes mit einem Würfelgitter",
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99:{\displaystyle \{e,a,a^{2},\dots ,a^{s-1}\}}
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257:: CS1 maint: location missing publisher (
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388:Publicationes Mathematicae Debrecen
359:Mathematical Association of America
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439:Conjectures that have been proved
247:(in German), Leipzig, p. 28
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313:American Mathematical Monthly
245:Diophantische Approximationen
310:(1974), "Algebraic tiling",
36:, that is, sets of the form
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205:Mathematische Zeitschrift
434:Theorems in group theory
24:states that if a finite
401:10.5486/PMD.1949.1.1.10
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28:is expressed as the
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218:10.1007/BF01180974
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368:978-0-88385-028-2
349:Stein, Sherman K.
195:{\displaystyle n}
159:Hermann Minkowski
119:{\displaystyle e}
30:Cartesian product
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279:(3–4): 329–373,
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180:Hajós, Georg
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132:György Hajós
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18:group theory
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212:: 427–467,
144:Tibor Szele
136:group rings
428:Categories
234:0025.25401
173:References
418:253650078
394:: 56–62,
384:Szele, T.
301:122838903
267:Rédei, L.
226:127629936
86:−
72:…
34:simplexes
253:citation
243:(1907),
128:subgroup
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377:1311249
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334:2318582
293:0186729
163:tilings
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106:where
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140:Rédei
363:ISBN
259:link
396:doi
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230:Zbl
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