Subgroup separability and 3-manifold groups

DOI10.1007/BF02571384zbMath0711.57002MaRDI QIDQ1812957

Graham A. Niblo, Darren D. Long

Publication date: 25 June 1992

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174265

zbMATH Keywords

amalgamated free productsseparable groups3-manifold groupsLerf 3-manifold groupsperipheral subgroups of a 3-manifold groupZ-amalgamated free product of two Lerf groups

Mathematics Subject Classification ID

Related Items (26)

Subgroup separability, knot groups and graph manifolds ⋮ The Hanna Neumann conjecture for surface groups ⋮ Some 3-manifolds and 3-orbifolds with large fundamental group ⋮ Relative cohomology theory for profinite groups ⋮ Graphs and separability properties of groups ⋮ Separable subsets of GFERF negatively curved groups. ⋮ Subgroup separable free products with cyclic amalgamation ⋮ Residual finiteness of infinite amalgamated products of cyclic groups. ⋮ Noncoherence of arithmetic hyperbolic lattices ⋮ Geodesic ideal triangulations exist virtually ⋮ Twisted Alexander polynomials detect fibered 3-manifolds ⋮ A 3-manifold with a non-subgroup-separable fundamental group ⋮ Separability properties of free groups and surface groups ⋮ Non-separable surfaces in cubed manifolds ⋮ Essential closed surfaces in bounded 3-manifolds ⋮ Link quandles are residually finite ⋮ Fixed subgroups of automorphisms of hyperbolic 3-manifold groups ⋮ Finite quotients of rings and applications to subgroup separability of linear groups ⋮ Engulfing in word-hyperbolic groups ⋮ Infinite Coxeter groups are virtually indicarle ⋮ Symplectic $\mathbf{S}^{1} \times N^3$, subgroup separability, and vanishing Thurston norm ⋮ Residual finiteness, QCERF and fillings of hyperbolic groups. ⋮ Free quandles and knot quandles are residually finite ⋮ $3$-Manifold Groups are Virtually Residually $p$ ⋮ A characterization of virtually embedded subsurfaces in $3$-manifolds ⋮ Howson property and one-relator groups¹

Cites Work

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• An example of a non-LERF group which is a free product of LERF groups with an amalgamated cyclic subgroup
• Immersions and Embeddings of Totally Geodesic Surfaces
• A note on groups with separable finitely generated subgroups
• Finite Covers of 3-Manifolds Containing Essential Surfaces of Euler Characteristic = 0
• Subgroups of Surface Groups are Almost Geometric

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