A note on groups with separable finitely generated subgroups

DOI10.1017/S0004972700026393zbMath0613.20018OpenAlexW2101435336MaRDI QIDQ3754172

D. Solitar, A. Karrass, Robert G. Burns

Publication date: 1987

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700026393

zbMATH Keywords

fundamental groupprofinite topologyone relator groupssubgroup separablethree-dimensional manifold

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Fundamental group, presentations, free differential calculus (57M05) Residual properties and generalizations; residually finite groups (20E26) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

Related Items (27)

Subgroup separability, knot groups and graph manifolds ⋮ Linear representations of binate groups ⋮ Abelian subgroup separability of certain generalized free products of free or finitely generated nilpotent groups. ⋮ Graphs and separability properties of groups ⋮ Knit products of some groups and their applications. ⋮ Separable subgroups of mapping class groups ⋮ Hydra group doubles are not residually finite. ⋮ Cubular tubular groups ⋮ Special cube complexes revisited: a quasi-median generalization ⋮ On subgroup separability of free‐by‐cyclic and deficiency 1 groups ⋮ Profinite rigidity of graph manifolds and JSJ decompositions of 3-manifolds ⋮ Strictly ascending HNN extensions in soluble groups. ⋮ Finite index subgroups of graph products. ⋮ Non-separable surfaces in cubed manifolds ⋮ On the Subgroup Separability of Generalized Free Products of Nilpotent Groups ⋮ On the profinite topology of right-angled Artin groups. ⋮ Engulfing in word-hyperbolic groups ⋮ Quasi-potency and cyclic subgroup separability. ⋮ Symplectic $\mathbf{S}^{1} \times N^3$, subgroup separability, and vanishing Thurston norm ⋮ Subgroup separability of HNN-extensions with Abelian base group ⋮ Profinite properties of graph manifolds ⋮ Residually finite tubular groups ⋮ Subgroup separability and 3-manifold groups ⋮ Subgroup Separability and Linearity of Certain Graphs of Groups ⋮ Around 3-manifold groups ⋮ Binate towers of groups ⋮ Howson property and one-relator groups¹

Cites Work

• Unnamed Item
• On Dehn's lemma and the asphericity of knots
• The isomorphism problem for one-relator groups with non-trivial centre
• An Improved Subgroup Theorem for HNN Groups with Some Applications
• The Subgroups of a Free Product of Two Groups with an Amalgamated Subgroup
• Finitely Generated 3-Manifold Groups are Finitely Presented

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