-изоморфизмы смешанных абелевых групп ранга
Schichtengleiche Gewichte und Butlergruppen
Self--injective abelian groups
Self-cancellation of torsion-free Abelian groups of finite rank.
Self-pseudoprojective completely decomposable Abelian groups.
Self-small products of abelian groups
Let and be two abelian groups. The group is called -small if the covariant functor commutes with all direct sums and is self-small provided it is -small. The paper characterizes self-small products applying developed closure properties of the classes of relatively small groups. As a consequence, self-small products of finitely generated abelian groups are described.
Semitopological homomorphisms
Separable and vector groups whose projectively invariant subgroups are fully invariant.
Separable mixed groups
Shelah's Singular Compactness Theorem.
Simple proofs of some generalizations of the Wilson’s theorem
In this paper a remarkable simple proof of the Gauss’s generalization of the Wilson’s theorem is given. The proof is based on properties of a subgroup generated by element of order 2 of a finite abelian group. Some conditions equivalent to the cyclicity of (Φ(n), ·n), where n > 2 is an integer are presented, in particular, a condition for the existence of the unique element of order 2 in such a group.
Simulated factorizations II.
Singular homology groups of one-dimensional Peano continua
Let X be a one-dimensional Peano continuum. Then the singular homology group H₁(X) is isomorphic to a free abelian group of finite rank or the singular homology group of the Hawaiian earring.
Skeletons, bodies and generalized -algebras
Slender modules, endo-slender abelian groups and large cardinals
Small almost free modules with prescribed topological endomorphism rings
Small-sum pairs in abelian groups
Let be an abelian group and two subsets of equal size such that and both have size . Answering a question of Bihani and Jin, we prove that if is aperiodic or if there exist elements and such that has a unique expression as an element of and has a unique expression as an element of , then is a translate of . We also give an explicit description of the various counterexamples which arise when neither condition holds.
Smooth invariants and -graded modules over
It is shown that every -graded module over is a direct sum of cyclics. The invariants for such modules are exactly the smooth invariants of valuated abelian -groups.
Solitary quotients of finite groups
We introduce and study the lattice of normal subgroups of a group G that determine solitary quotients. It is closely connected to the well-known lattice of solitary subgroups of G, see [Kaplan G., Levy D., Solitary subgroups, Comm. Algebra, 2009, 37(6), 1873–1883]. A precise description of this lattice is given for some particular classes of finite groups.
Solution générale sur un groupe abélien de l'équation fonctionelle f(x*f(y)) = f(f(x)*y).