منابع مشابه
Dominions in varieties of nilpotent groups
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...
متن کاملDominions 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 varieties generated by simple groups
Let S be a nite nonabelian simple group, and let H be a subgroup of S. In this work, the dominion (in the sense of Isbell) of H in S in Var(S) is determined, generalizing an example of B.H. Neumann. A necessary and suucient condition for H to be epimorphically embedded in S is obtained. These results are then extended to a variety generated by a family of nite nonabelian simple groups. An epimo...
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...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2000
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870008826892