Subgroups of free 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 کاملSubgroups of Free Metabelian Groups
In 1954 A. G. Howson proved that the intersection of two finitely generated subgroups of a free group is again finitely generated. Now the free metabelian subgroups of a free metabelian group of finite rank n are quite restricted. Indeed they are again of finite rank at most n. This suggests that there may be an analog of Howson’s theorem for free metabelian groups. This turns out not to be the...
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: Journal of the Australian Mathematical Society
سال: 1971
ISSN: 0004-9735
DOI: 10.1017/s1446788700009423