منابع مشابه
Separability 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 کاملA-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 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 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 کاملComputing Subgroups by Exhibition in Finite Solvable Groups
Subgroups such as Hall systems, system normalizers, F-normalizers and F-covering subgroups arise naturally in the study of finite solvable groups. Here we present practical algorithms to compute such subgroups. Besides being of interest in the theory of formations, the algorithms also yield fast methods for constructing head complements. These complements are closely related to the maximal subg...
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: International Journal of Algebra and Computation
سال: 2015
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196715500253