Isomorphic subgroups of solvable groups
نویسندگان
چکیده
منابع مشابه
A-Generated Subgroups of A-Solvable Groups
In the discussion of A-solvable groups, the question arises if a torsion-free abelian group A of finite rank is flat as a module over its endomorphism ring if every A-generated subgroup of a torsion-free A-solvable group is A-solvable. This paper gives a negative answer by constructing a torsion-free group of rank 3 for which all A-generated torsion-free groups are A-solvable, although A is not...
متن کاملSuperrigid Subgroups of Solvable Lie Groups
Let Γ be a discrete subgroup of a simply connected, solvable Lie group G, such that AdG Γ has the same Zariski closure as AdG. If α : Γ → GLn(R) is any finite-dimensional representation of Γ, we show that α virtually extends to a continuous representation σ of G. Furthermore, the image of σ is contained in the Zariski closure of the image of α. When Γ is not discrete, the same conclusions are t...
متن کاملSeparability of Solvable Subgroups in Linear Groups
Let Γ be a finitely generated linear group over a field of characteristic 0. Suppose that every solvable subgroup of Γ is polycyclic. Then any solvable subgroup of Γ is separable. This conclusion is false without the hypothesis that every solvable subgroup of Γ is polycyclic.
متن کاملSolvable Groups with Many Bfc-subgroups
We characterize the solvable groups without infinite properly ascending chains of non-BFC subgroups and prove that a non-BFC group with a descending chain whose factors are finite or abelian is a Černikov group or has an infinite properly descending chain of non-BFC subgroups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2015
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/12534