Almost all one-relator groups with at least three generators are residually finite.

DOI10.4171/JEMS/255zbMath1225.20032arXiv0809.4693OpenAlexW2002295808MaRDI QIDQ621852

Iva Špakulová, Mark V. Sapir

Publication date: 28 January 2011

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.4693

zbMATH Keywords

finitely generated subgroupsone-relator groupsresidually finite groupsascending HNN extensionsrandom groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Residual properties and generalizations; residually finite groups (20E26) Probabilistic methods in group theory (20P05)

Related Items (9)

2-polyhedra for which every homotopy domination over itself is a homotopy equivalence ⋮ Primitivity rank for random elements in free groups ⋮ ℓ2$\ell ^2$‐Betti numbers and coherence of random groups ⋮ Uniform negative immersions and the coherence of one-relator groups ⋮ Root extraction in one-relator groups and slenderness ⋮ Non-Noetherian groups and primitivity of their group algebras ⋮ Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groups ⋮ Conjugacy and Other Properties of One-Relator Groups ⋮ Asymptotic invariants, complexity of groups and related problems

Cites Work

• Unnamed Item
• Unnamed Item
• A random tunnel number one 3-manifold does not fiber over the circle
• Generic properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups.
• Trees, valuations, and the Bieri-Neumann-Strebel invariant
• Smoothness of the convex hull of planar Brownian motion
• Mapping tori of free group automorphisms are coherent
• Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms
• Reflections on the residual finiteness of one-relator groups.
• Polynomial Maps over p -Adics and Residual Properties of Mapping Tori of Group Endomorphisms
• Brownian Excursions from Hyperplanes and Smooth Surfaces
• Some two-generator one-relator non-Hopfian groups
• The SQ-universality of hyperbolic groups
• The residual finiteness of positive one-relator groups

This page was built for publication: Almost all one-relator groups with at least three generators are residually finite.