An axiomatic approach for the Hajós theorem.
An orthogonal theory of a set-valued bifunctor
Butler groups of infinite rank and axiom 3
Butler groups splitting over a base element
We characterize a particular kind of decomposition of a Butler group that is the general case for Butler B(1)-groups; and exhibit a decomposition of a B(2)-group which is not of that kind.
Butler groups, valuated vector spaces, and duality
Completely decomposable abelian groups any regular subgroup of which is completely decomposable
Completely decomposable pure subgroups of completely decomposable abelian groups
Conservation Rules of Direct Sum Decomposition of Groups
In this article, conservation rules of the direct sum decomposition of groups are mainly discussed. In the first section, we prepare miscellaneous definitions and theorems for further formalization in Mizar [5]. In the next three sections, we formalized the fact that the property of direct sum decomposition is preserved against the substitutions of the subscript set, flattening of direct sum, and layering of direct sum, respectively. We referred to [14], [13] [6] and [11] in the formalization.
Cube tilings as contributions of algebra to geometry.
Das Gewicht einer Butlergruppe.
Decompositions of local rigid ACD groups
We study direct decompositions of extensions of rigid completely decomposable groups by finite primary groups. These decompositions are unique and can be found by finite procedures. By passing to certain quotients the determination of the direct decompositions is made more efficient.
Die Struktur kartesischer Produkte ganzer Zahlen modulo kartesische Produkte ganzer Zahlen.
Direct decompositions of uniform groups
Uniform groups are extensions of rigid completely decomposable groups by a finite direct sum of cyclic primary groups all of the same order. The direct decompositions of uniform groups are completely determined by an algorithm that is realised by a MAPLE procedure.
Ein gruppentheoretisches Kriterium für die Lösbarkeit der Funktionalgleichung f(x + y) =F(f(x),f(y))
Equivalent Expressions of Direct Sum Decomposition of Groups1
In this article, the equivalent expressions of the direct sum decomposition of groups are mainly discussed. In the first section, we formalize the fact that the internal direct sum decomposition can be defined as normal subgroups and some of their properties. In the second section, we formalize an equivalent form of internal direct sum of commutative groups. In the last section, we formalize that the external direct sum leads an internal direct sum. We referred to [19], [18] [8] and [14] in the...
Erratum “Pure extensions of locally compact abelian groups” [Rend. Sem. Mat. Univ. Padova 116 (2006), 31–40]
Essentially Rigid Floppy Subgroups of the Baer-Specker Group.
Evasion and prediction - the Specker phenomenon and Gross space.
Factoring Groups and Tiling Space
Factor-splitting Abelian groups of arbitrary rank