A short proof of Eilenberg and Moore’s theorem
In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.
Active sums I.
Given a generating family F of subgroups of a group G closed under conjugation and with partial order compatible with inclusion, a new group S can be constructed, taking into account the multiplication in the subgroups and their mutual actions given by conjugation. The group S is called the active sum of F, has G as a homomorph and is such that S/Z(S) ≅ G/Z(G) where Z denotes the center.The basic question we investigate in this paper is: when is the active sum S of the family F isomorphic to the...
-тождества и -многообразия
-тождества нильпотентных групп. I
-тождества нильпотентных групп. II
On Amalgamated Products of Profinite Groups.
On localizations of torsion abelian groups
As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of LT is bounded by whenever T is torsion abelian and L is a localization functor. In this paper we study localizations of torsion abelian groups and investigate new examples. In particular we prove that the structure of LT is determined by the structure of the localization of the primary components of T in many cases. Furthermore, we completely characterize the relationship...
On projective and injective objects of the categories dual to .
On prosolvable subgroups of profinite free products and some applications.
On the existence of group localizations under large-cardinal axioms.
Uno de los problemas abiertos más antiguos de la teoría de grupos categórica es si todo par ortogonal (formado por una clase de grupos y una clase de homomorfismos que se determinan mutuamente por ortogonalidad en el sentido de Freyd-Kelly), se halla asociado a un funtor de localización. Se sabe que esto es cierto si se acepta la validez de un cierto axioma de cardinales grandes (el principio de Vopenka), pero no se conoce ninguna demostración mediante los axiomas ordinarios (ZFC) de la teoría de...
On the Genus of a Nilpotent Group with Finite Commutator Subgroup.
Relation modules of finite groups and related topics.
Remarks on the Mal'cev completion of torsion-free locally nilpotent groups
Splitting classes in categories of groups.
The envelope of a subcategory in topology and group theory.
The Roquette category of finite -groups
Let be a prime number. This paper introduces the Roquette category of finite -groups, which is an additive tensor category containing all finite -groups among its objects. In , every finite -group admits a canonical direct summand , called the edge of . Moreover splits uniquely as a direct sum of edges of Roquette -groups, and the tensor structure of can be described in terms of such edges. The main motivation for considering this category is that the additive functors from to...
The strong amalgamation property and (effective) codescent morphisms.
The...-CATEGORY OF A SEMIGROUP.
Un théorême sur les sommes amalgamées de groupes simpliciaux.
Varietal generalisations of Schur multipliers, stem extensions and stem covers.