Some fourth degree Diophantine equations in Gaussian integers.
Factorizations and Paige's theorem on complete maps.
Hajós' theorem and the partition lemma.
The Diophantine equation in three quadratic fields.
Cube tilings as contributions of algebra to geometry.
Tiling 3 and 4-dimensional Euclidean spaces by Lee spheres
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.
A Rédei type factorization result for a special 2-group.
The size of an annihilator in a factorization.
A Hajós-type result on factoring finite Abelian groups by subsets.
Factoring Abelian groups of order .
An axiomatic approach for the Hajós theorem.
Factorization results with combinatorial proofs.
Factoring a finite Abelian group by prime complexes.
Factoring by nonsubgroup factors.
The possibility of extending factorization results to infinite Abelian groups.
Multiple tilings by cubes with no shared faces.
On a problem of A.D. Sands.
Some problems on splittings of groups.
Abelian groups that cannot be factored without periodic factor
Factoring an odd abelian group by lacunary cyclic subsets
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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