منابع مشابه
Zariski closures and subgroup separability
The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of ...
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In this note, we give characterizations for certain HNN extensions of polycyclic-by-finite groups with central associated subgroups to be subgroup separable and conjugacy separable. We shall do this by showing the equivalence of subgroup separability and conjugacy separability in this type of HNN extensions. 2000 Mathematics Subject Classification: Primary 20E06, 20E26; Secondary 20F10, 20F19
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We begin by recalling that if Γ is a group, andH a subgroup of Γ, then Γ is calledH-separable if for every g ∈ Γ\H, there is a subgroup K of finite index in Γ such that H ⊂ K but g / ∈ K. The group Γ is called subgroup separable (or LERF) if Γ is H-separable for all finitely generated subgroups H. As is well-known LERF is a powerful property in the setting of low-dimensional topology which has ...
متن کاملSubgroup Separability in Residually Free Groups
We prove that the finitely presentable subgroups of residually free groups are separable and that the subgroups of type FP∞ are virtual retracts. We describe a uniform solution to the membership problem for finitely presentable subgroups of residually free groups.
متن کاملPTL-separability and closures for WQOs on words
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of upward closed sets. In this way, a range of regular language classes arises as PTLs. Moreover, each of the WQOs guarantees regularity of all downward closed se...
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2017
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-016-0300-8