Virtual retraction and Howson’s theorem in pro-$p$ groups

DOI10.1090/tran/7784zbMath1480.20077arXiv1705.09096OpenAlexW2964028471MaRDI QIDQ5217873

Mark Shusterman, Pavel A. Zalesskii

Publication date: 26 February 2020

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.09096

Mathematics Subject Classification ID

Geometric group theory (20F65) Asymptotic properties of groups (20F69) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Limits, profinite groups (20E18)

Related Items (4)

Pro-\(p\) groups acting on trees with finitely many maximal vertex stabilizers up to conjugation ⋮ Demushkin groups of uncountable rank ⋮ Inertia of retracts in Demushkin groups ⋮ Galois module structure of the units modulo \(p^m\) of cyclic extensions of degree \(p^n\)

Cites Work

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• Ascending chains of finitely generated subgroups
• On the rank of the intersection of free subgroups in virtually free groups.
• The Sylow subgroups of the absolute Galois group \(\mathrm{Gal}(\mathbb{Q})\)
• On pro-\(p\) analogues of limit groups via extensions of centralizers.
• Intersection of finitely generated surface groups
• Submultiplicativity and the Hanna Neumann conjecture.
• On the Howson property of HNN-extensions with Abelian base group and amalgamated free products of Abelian groups.
• The structure of free prosupersolvable groups
• On a new characterization of Demuskin groups
• Demuškin groups, Galois modules, and the elementary type conjecture
• Finitely presented wreath products and double coset decompositions.
• Finite index subgroups of graph products.
• Fully residually free pro-\(p\) groups.
• Subgroup separability and virtual retractions of groups
• Intersections of finitely generated subgroups of free groups and resolutions of graphs
• Combinatorial group theory for pro-p groups
• Virtually free factors of pro-\(p\) groups
• Pro-2-Demuškin groups of rank \({\aleph{}}_ 0\) as Galois groups of maximal 2-extensions of fields
• Demuškin groups of rank \(\aleph{}_ 0\) as absolute Galois groups
• On the intersection of subgroups of a free group
• On prosupersolvable groups
• Finitely generated pro-\(p\) absolute Galois groups over global fields
• Finitely generated groups with the M. Hall property
• Equivalence of the strengthened Hanna Neumann conjecture and the amalgamated graph conjecture
• Almost free groups and the M. Hall property
• Pro-\(p\) Galois groups of rank \(\leq 4\)
• Examples of retracts in free groups that are not the fixed subgroup of any automorphism.
• Combination of convergence groups.
• Demuškin fields with valuations
• Virtually free pro-\(p\) products
• Free-by-Demushkin pro-\(p\) groups.
• Epimorphisms of Demushkin groups
• Towards the Hanna Neumann conjecture using Dicks' method
• Cohomologie galoisienne. Cours au Collège de France, 1962--1963. Seconde édition.
• Approximation by subgroups of finite index and the Hanna Neumann conjecture
• Hall's theorem for limit groups.
• On a conjecture of Karrass and Solitar.
• Special cube complexes
• On the Kurosh rank of the intersection of subgroups in free products of groups.
• Varieties of finite supersolvable groups with the M.~Hall property.
• Sur la dimension cohomologique des groupes profinis
• On the intersection of finitely generated subgroups of a free group
• The rank three case of the Hanna Neumann Conjecture
• SUBDIRECT PRODUCTS OF FREE PRO-p AND DEMUSHKIN GROUPS
• Schreier’s formula for prosupersolvable groups
• SUBGROUPS OF PROFINITE GROUPS ACTING ON TREES
• THE TOPOLOGY AND ANALYSIS OF THE HANNA NEUMANN CONJECTURE
• On a theorem of Peter Scott
• Verbally closed subgroups of free groups
• On Demuskin groups with involution
• Discrete Groups of Motions
• Field Arithmetic
• On the intersection of free subgroups in free products of groups
• Graphs, free groups and the Hanna Neumann conjecture
• Intersections of finitely generated free groups
• 3-Manifold Groups with the Finitely Generated Intersection Property
• Covering space proofs in combinatorial group theory
• Groups in which every Finitely Generated Subgroup is almost a Free Factor
• Subgroups of Surface Groups are Almost Geometric
• Amalgamated Products and the Howson Property
• A property of subgroups of infinite index in a free group
• Verbally closed virtually free subgroups
• Groups with positive rank gradient and their actions
• SUBGROUPS AND HOMOLOGY OF FREE PRODUCTS OF PROFINITE GROUPS
• INTERSECTING FREE SUBGROUPS IN FREE PRODUCTS OF GROUPS
• Profinite Graphs and Groups
• Subgroup properties of Demushkin groups
• Hyperplane sections in arithmetic hyperbolic manifolds
• Detecting pro-p-groups that are not absolute Galois groups
• A Karrass–Solitar theorem for profinite groups
• Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture: with an Appendix by Warren Dicks
• Intersections of Finitely Generated Subgroups in Free Products
• Classification of Demushkin Groups
• Demuškin groups of rank $\aleph_0$
• On Finitely Generated Subgroups of Free Products
• The Subgroups of a Free Product of Two Groups with an Amalgamated Subgroup
• Finitely Generated Subgroups of HNN Groups
• On the Finitely Generated Subgroups of an Amalgamated Product of Two Groups
• Coset Representations in Free Groups
• On the Intersection of Finitely Generated Free Groups
• Absolute retracts in group theory
• Profinite Groups

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