Covering abelian groups with cyclic subsets.
Differences in sets of lengths of Krull monoids with finite class group
Let be a Krull monoid with finite class group where every class contains some prime divisor. It is known that every set of lengths is an almost arithmetical multiprogression. We investigate which integers occur as differences of these progressions. In particular, we obtain upper bounds for the size of these differences. Then, we apply these results to show that, apart from one known exception, two elementary -groups have the same system of sets of lengths if and only if they are isomorphic.
Ein Satz über abelsche Gruppen mit Anwendungen auf die Geometrie der Zahlen.
Eine gruppentheoretische Methode in der Musiktheorie
Elementary Abelian p-groups as Automorphism Groups of Infinite Groups. I.
Endomorphism kernel property for finite groups
A group has the endomorphism kernel property (EKP) if every congruence relation on is the kernel of an endomorphism on . In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian groups which have EKP.
Erratum to: “Solitary quotients of finite groups”
In this short note a correct proof of Theorem 3.3 from [Tărnăuceanu M., Solitary quotients of finite groups, Cent. Eur. J. Math., 2012, 10(2), 740–747] is given.
Factoring a finite Abelian group by prime complexes.
Factoring Abelian groups of order .
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.
Factoring by nonsubgroup factors.
Factorization results with combinatorial proofs.
Factorizations and Paige's theorem on complete maps.
Finite abelian groups and factorization problems
Finite abelian groups and factorization problems. II
Generalizations of Cole's Systems
There are four resolvable Steiner triple systems on fifteen elements. Some generalizations of these systems are presented here.
Graph representations of finite Abelian groups
Graphs of finite abelian groups
Hajós' theorem and the partition lemma.
Index Transforms for Multidimensional DFT's and Convolutions.