Add to ORKGThe study of groups available as products of two Abelian subgroups was, if not initiated, so speeded up with the well known and remarkable result of Ito: Any such a product is soluble of length at most 2. Many new results have been added during the last decades and a need to write a comprehensive treatment on the aforementioned subject appeared. The presented doctoral thesis collects many more or less known results on products, the exposition is unified and, in many cases, the theorems are supplied with new proofs. Besides, new results on products of cyclic groups are added. Moreover, an introduction to the theory of commutative radical rings and a generalization to connected transversals are included.Available from STL Prague, CZ / NTK - N...
Summary. In this article, we formalize that every finite cyclic group is isomorphic to a direct prod...
Summary. In the first section we present properties of fields and Abelian groups in terms of commuta...
We outline results on varieties of groups generated by Cartesian and direct wreath products of abeli...
Answering a generalized version of G. Choquet's problem, various theorems characterizing the minimal...
AbstractThe t-product of a family {Gi}iϵI of abelian p-groups is the torsion subgroup of ΠiϵIGi, whi...
AbstractWe investigate products of finite abelian groups of bounded exponent as profinite structures...
The concept of a free group is discussed first in Chapter 1 and in Chapter 2 the tensor product of t...
This thesis deals with the formalisation of some group-theoretic results in Isabelle/HOL – an intera...
summary:Let $A$ and $B$ be two abelian groups. The group $A$ is called $B$-small if the covariant fu...
The study of finite groups factorised as a product of two or more subgroups has become a subject of ...
It is unknown whether every group G = AB which is the product of of two abelian-by-finite subgroups ...
AbstractWe consider finite groups which have connected transversals to subgroups whose order is a pr...
The semidirect product of groups is a generalization of the direct product construction and provides...
Let the group G = AB be a product of two π-decomposable sub-groups A = Oπ(A) × Oπ' (A) and B = Oπ(B)...
The work presents results concerning the self-smallness and relative smallness properties of product...
Summary. In this article, we formalize that every finite cyclic group is isomorphic to a direct prod...
Summary. In the first section we present properties of fields and Abelian groups in terms of commuta...
We outline results on varieties of groups generated by Cartesian and direct wreath products of abeli...
Answering a generalized version of G. Choquet's problem, various theorems characterizing the minimal...
AbstractThe t-product of a family {Gi}iϵI of abelian p-groups is the torsion subgroup of ΠiϵIGi, whi...
AbstractWe investigate products of finite abelian groups of bounded exponent as profinite structures...
The concept of a free group is discussed first in Chapter 1 and in Chapter 2 the tensor product of t...
This thesis deals with the formalisation of some group-theoretic results in Isabelle/HOL – an intera...
summary:Let $A$ and $B$ be two abelian groups. The group $A$ is called $B$-small if the covariant fu...
The study of finite groups factorised as a product of two or more subgroups has become a subject of ...
It is unknown whether every group G = AB which is the product of of two abelian-by-finite subgroups ...
AbstractWe consider finite groups which have connected transversals to subgroups whose order is a pr...
The semidirect product of groups is a generalization of the direct product construction and provides...
Let the group G = AB be a product of two π-decomposable sub-groups A = Oπ(A) × Oπ' (A) and B = Oπ(B)...
The work presents results concerning the self-smallness and relative smallness properties of product...
Summary. In this article, we formalize that every finite cyclic group is isomorphic to a direct prod...
Summary. In the first section we present properties of fields and Abelian groups in terms of commuta...
We outline results on varieties of groups generated by Cartesian and direct wreath products of abeli...