On a class of abelian p-groups.
On a class of Butler groups.
On a class of locally Butler groups
A torsionfree abelian group is called a Butler group if for any torsion group . It has been shown in [DHR] that under any countable pure subgroup of a Butler group of cardinality not exceeding is again Butler. The purpose of this note is to show that this property has any Butler group which can be expressed as a smooth union of pure subgroups having countable typesets.
On a class of locally completely decomposable Abelian groups
On a class of torsionfree Abelian groups [Abstract of thesis]
On A Combinatorial Problem Connected withFactorizations
On a complete set of operations for factorizing codes
It is known that the class of factorizing codes, i.e., codes satisfying the factorization conjecture formulated by Schützenberger, is closed under two operations: the classical composition of codes and substitution of codes. A natural question which arises is whether a finite set of operations exists such that each factorizing code can be obtained by using the operations in and starting with prefix or suffix codes. is named here a complete set of operations (for factorizing codes). We show...
On a complete set of operations for factorizing codes
It is known that the class of factorizing codes, i.e., codes satisfying the factorization conjecture formulated by Schützenberger, is closed under two operations: the classical composition of codes and substitution of codes. A natural question which arises is whether a finite set O of operations exists such that each factorizing code can be obtained by using the operations in O and starting with prefix or suffix codes. O is named here a complete set of operations (for factorizing codes). We show...
On a conjecture of Erdös and Heilbronn
On a conjecture of Hamidoune for subsequence sums.
On a connection of number theory with graph theory
We assign to each positive integer a digraph whose set of vertices is and for which there is a directed edge from to if . We establish necessary and sufficient conditions for the existence of isolated fixed points. We also examine when the digraph is semiregular. Moreover, we present simple conditions for the number of components and length of cycles. Two new necessary and sufficient conditions for the compositeness of Fermat numbers are also introduced.
On a generalization of a Prüfer-Kaplansky-Procházka theorem
On a generalization of Mycielski's and Znám's conjectures about coset decomposition of Abelian groups
On a problem of A.D. Sands.
On a variation of Sands' method.
On abelian groups by which balanced extensions of a rational group split. II
On additive bases
On additive bases with two elements
On Butler -groups decomposing over two base elements
A -group is a sum of a finite number of torsionfree Abelian groups of rank , subject to two independent linear relations. We complete here the study of direct decompositions over two base elements, determining the cases where the relations play an essential role.
On Cartesian Powers of a Rational Group.