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Tiling 3 and 4-dimensional Euclidean spaces by Lee spheres

Szabó, Sándor — 2014

Serdica Mathematical Journal

The paper addresses the problem if the n-dimensional Euclidean space can be tiled with translated copies of Lee spheres of not necessarily equal radii such that at least one of the Lee spheres has radius at least 2. It will be showed that for n = 3, 4 there is no such tiling. 2010 Mathematics Subject Classification: Primary 94B60; Secondary 05B45, 52C22.

Factoring an odd abelian group by lacunary cyclic subsets

Sándor Szabó — 2010

Discussiones Mathematicae - General Algebra and Applications

It is a known result that if a finite abelian group of odd order is a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper gives an elementary proof that does not rely on characters.

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