Detecting large groups.

DOI10.1016/j.jalgebra.2010.07.012zbMath1231.20026arXivmath/0702571OpenAlexW1978502032MaRDI QIDQ619020

Marc Lackenby

Publication date: 21 January 2011

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702571

zbMATH Keywords

subgroups of finite indexfree groupsfinitely presented groupsprofinite completionshomology groupsBetti numbersderived seriescentral serieslarge groups\(p\)-large groupsweakly parafree groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Topological methods in group theory (57M07) Homological methods in group theory (20J05) Chains and lattices of subgroups, subnormal subgroups (20E15) Free nonabelian groups (20E05) Derived series, central series, and generalizations for groups (20F14) Limits, profinite groups (20E18)

Related Items

GOLOD–SHAFAREVICH GROUPS: A SURVEY ⋮ Homology torsion growth of finitely presented pro-p groups ⋮ Prefrattini subgroups and crowns ⋮ Stability for product groups and property \(( \tau )\) ⋮ On profinite groups with positive rank gradient ⋮ Finding disjoint surfaces in 3-manifolds ⋮ Mod-\(p\) cohomology growth in \(p\)-adic analytic towers of 3-manifolds ⋮ Pro‐p groups of positive rank gradient and Hausdorff dimension ⋮ Detecting ends of residually finite groups in profinite completions ⋮ APPLICATIONS OF p-DEFICIENCY AND p-LARGENESS ⋮ Groups of p-deficiency one

Cites Work

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• New lower bounds on subgroup growth and homology growth
• Large groups, property (τ) and the homology growth of subgroups
• Essential closed surfaces in bounded 3-manifolds
• Groups with the same lower Central Sequence as a Relatively Free Group. I The Groups
• Groups with the Same lower Central Sequence as a Relatively Free Group. II. Properties
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