Sia un primo, e un gruppo abeliano elementare di ordine che agisce sul -gruppo localmente finito . Supponiamo che esista un intero positivo tale che per ogni . In questo articolo si dimostra che è nilpotente, con classe di nilpotenza limitata da una funzione che dipende solo da e .
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...
Nous montrons que le sous-groupe des points fixes d’un automorphisme d’un groupe hyperbolique au sens de M. Gromov est de type fini.
In this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if is an automorphism of order four of a polycyclic group and the map defined by is surjective, then contains a characteristic subgroup of finite index such that the second derived subgroup is included in the centre of and is abelian, both and are abelian-by-finite. These results extend recent and classical results in the literature....
In this paper, we give a generalization of Baer Theorem on the injective property of divisible abelian groups. As consequences of the obtained result we find a sufficient condition for a group to express as semi-direct product of a divisible subgroup and some subgroup . We also apply the main Theorem to the -groups with center of index , for some prime . For these groups we compute the number of conjugacy classes and the number of abelian maximal subgroups and the number of nonabelian...