Dominions in varieties of nilpotent groups
نویسندگان
چکیده
The concept of dominion (in the sense of Isbell) is investigated in several varieties of nilpotent groups. A complete description of dominions in the variety of nilpotent groups of class at most 2 is given, and used to prove nontriviality of dominions in the variety of nilpotent groups of class at most c for any c>1 . Some subvarieties of N2 , and the variety of all nilpotent groups of class at most c and exponent p , where p is a prime greater than c , are also studied. The behavior of dominions of subgroups of groups in N2 when taken in the contex of Nc for c>2 is investigated. Finally, nontriviality of dominions in any locally nilpotent torsionfree variety of groups is established. Section
منابع مشابه
Dominions in finitely generated nilpotent groups
In the first part, we prove that the dominion (in the sense of Isbell) of a subgroup of a finitely generated nilpotent group is trivial in the category of all nilpotent groups. In the second part, we show that the dominion of a subgroup of a finitely generated nilpotent group of class two is trivial in the category of all metabelian nilpotent groups. Section
متن کاملDominions in decomposable varieties
Dominions, in the sense of Isbell, are investigated in the context of decomposable varieties of groups. An upper and lower bound for dominions in such a variety is given in terms of the two varietal factors, and the internal structure of the group being analyzed. Finally, the following result is established: If a variety N has instances of nontrivial dominions, then for any proper subvariety Q ...
متن کاملDominions in product varieties
Dominions, in the sense of Isbell, are investigatedin the contextof decomposable varieties of groups. An upper and lower bound for dominions in such a variety is given in terms of the two varietal factors, and the internal structure of the group being analyzed. Finally, the following result is established: If a variety N has instances of nontrivial dominions, then for any proper subvariety Q of...
متن کاملArea de la Investigación Científica Circuito Exterior
Dominions, in the sense of Isbell, are investigated in the context of decomposable varieties of groups. An upper and lower bound for dominions in such a variety is given in terms of the two varietal factors, and the internal structure of the group being analyzed. Finally, the following result is established: If a variety N has instances of nontrivial dominions, then for any proper subvariety Q ...
متن کامل