Classification of fibred group extensions and H...
Clinic obstructions and clinic cohomological groups.
Combins of Semidrect Products and 3-Manifold Groups.
Complements, baseless subgroups and sylow subgroups of infinite wreath products
Complements of Connected Subgroups in Algebraic Groups
Complete growth series and products of 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.
Contributions to the theory of decompositions on a group
Crossed modules, Crossed n-fold extension of groups and Cohomology theory in Abstract Categories
Crossed product of cyclic groups
All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.
(Cyclic) subgroup separability of HNN and split extensions
Definition and Properties of Direct Sum Decomposition of Groups1
In this article, direct sum decomposition of group is mainly discussed. In the second section, support of element of direct product group is defined and its properties are formalized. It is formalized here that an element of direct product group belongs to its direct sum if and only if support of the element is finite. In the third section, product map and sum map are prepared. In the fourth section, internal and external direct sum are defined. In the last section, an equivalent form of internal...
Définition de l'intégrale de Feynman et processus à sauts
Depth and the Cohomology of Wreath Products.
Ends of groups and baseless subgroups of wreath products
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 to : “Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel–Leader graphs”
Extension of complexes of groups
Complexes of groups over ordered simplicial complexes are generalizations to higher dimensions of graphs of groups. We first relate them to complexes of spaces by considering their classifying space . Then we develop their homological algebra aspects. We define the notions of homology and cohomology of a complex of groups with coefficients in a -module and show the existence of free resolutions. We apply those notions to study extensions of complexes of groups with constant or abelian kernel....
Extensions centrales de groupes algébriques simplement connexes et cohomologie galoisienne
Extensions of abelian by hyper-(cyclic or finite) groups (II)