Finite and infinite cyclic extensions of free groups

DOI10.1017/S1446788700015445zbMath0299.20024WikidataQ60304261 ScholiaQ60304261MaRDI QIDQ4053811

A. Karrass, D. Solitar, Alfred Pietrowski

Publication date: 1973

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

Mathematics Subject Classification ID

Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06)

Related Items (84)

Geometric characterizations of virtually free groups ⋮ Finite groups of automorphisms of free groups ⋮ Free actions on handlebodies ⋮ On Cayley graphs of virtually free groups ⋮ FREE GROUP ROOTS OF a^kb^l AND [ a^k,b] ⋮ Conjugacy distinguished subgroups. ⋮ Sufficient and necessary conditions for hereditarity of infinite category algebras ⋮ Imbeddings of free actions on handlebodies ⋮ A virtually free pro-\(p\) need not be the fundamental group of a profinite graph of finite groups. ⋮ A Characterization of Periodic Automorphisms of a Free Group ⋮ Virtual Retraction Properties in Groups ⋮ Finite subgroups of groups of outer automorphisms of free groups ⋮ Combinatorial classification of finitely generated virtually free groups ⋮ The Weakly Potency of Certain HNN Extensions of Nilpotent Groups ⋮ Manifold covers of 3-orbifolds with geometric pieces ⋮ On the rational subset problem for groups. ⋮ Actions of finite groups of graphs and related automorphisms of free groups ⋮ Commensurability of groups quasi-isometric to RAAGs ⋮ The isomorphism problem for finite extensions of free groups is in PSPACE ⋮ Free products with amalgamation of finite groups and finite outer automorphism groups of free groups ⋮ Virtually free pro-\(p\) groups. ⋮ Verbally closed virtually free subgroups ⋮ Minsky Machines and Algorithmic Problems ⋮ The order of the automorphism group of a \(p\)-adic Schottky curve ⋮ The profinite completion of accessible groups ⋮ The Bass-Serre theorem revisited ⋮ On the rank of the intersection of free subgroups in virtually free groups. ⋮ Finitely generated \(p\)-adic discontinuous groups ⋮ Vertex separators, chordality and virtually free groups ⋮ \(C^\ast\)-stability of discrete groups ⋮ Incommensurable lattices in Baumslag–Solitar complexes ⋮ Genus for groups. ⋮ On a geometric description of \(\text{Gal}(\bar{\mathbb Q}_p/\mathbb Q_p)\) and a \(p\)-adic avatar of \(\widehat{GT}\) ⋮ Virtually free groups and integral representations ⋮ On Some Finiteness Properties in Infinite Groups ⋮ Graphs and groups with tree-like properties ⋮ Periodic automorphisms of free groups ⋮ On groups presented by inverse-closed finite confluent length-reducing rewriting systems ⋮ A new family of representations of virtually free groups ⋮ Infinite groups ⋮ Group actions on nonclosed 2-manifolds ⋮ Normalizers in groups and in their profinite completions. ⋮ Finiteness results for subgroups of finite extensions. ⋮ Dimension rigidity of lattices in semisimple Lie groups ⋮ Solutions to twisted word equations and equations in virtually free groups ⋮ The asymptotic geometry of right-angled Artin groups. I. ⋮ Virtually free groups with finitely many outer automorphisms ⋮ Mumford curves and Mumford groups in positive characteristic ⋮ Gilman's conjecture ⋮ On the virtually cyclic dimension of mapping class groups of punctured spheres ⋮ Nielsen realization by gluing: limit groups and free products ⋮ A subgroup formula for f-invariant entropy ⋮ Covering theory for graphs of groups ⋮ CONTEXT-FREE GROUPS AND THEIR STRUCTURE TREES ⋮ Subgroup conjugacy separability of free-by-finite groups. ⋮ A Necessary Condition for an Elliptic Element to Belong to a Uniform Tree Lattice ⋮ Groups with one more generator than relators ⋮ Determining whether a finite group of outer automorphisms of a free group is geometric. ⋮ Groups with one more generator than relators ⋮ Groups and NTS languages ⋮ Unnamed Item ⋮ Special groups with an elementary hierarchy are virtually free-by-\(\mathbb Z\). ⋮ On the existence of a free subgroup of finite index ⋮ Infinitely generated pseudocompact modules for finite groups and Weiss' theorem ⋮ On commensurability of right-angled Artin groups II: RAAGs defined by paths ⋮ A Counterexample to the Deformation Conjecture For Uniform Tree Lattices ⋮ Subgroup separability of certain HNN extensions ⋮ Splitting theorems for pro-\(p\) groups acting on pro-\(p\) trees ⋮ Residually finite tubular groups ⋮ Rational discrete first degree cohomology for totally disconnected locally compact groups ⋮ A uniqueness decomposition theorem for actions of finite groups on free groups ⋮ Finite extensions of free pro-\(p\) groups of rank at most two ⋮ The geometric dimension of an equivalence relation and finite extensions of countable groups ⋮ Rewriting systems, plain groups, and geodetic graphs ⋮ The isomorphism problem for one-relator groups with non-trivial centre ⋮ Algorithmic problems for amalgams of finite semigroups ⋮ On finite groups of isometries of handlebodies in arbitrary dimensions and finite extensions of Schottky groups ⋮ Groups, the theory of ends, and context-free languages ⋮ Cyclic extensions of free pro-\(p\) groups ⋮ Orientation-reversing free actions on handlebodies ⋮ Equivariant dimensions of groups with operators ⋮ A Geometric Proof of the Structure Theorem for Cyclic Splittings of Free Groups ⋮ Generalizing Magnus' Characterization of Free Groups to Some Free Products ⋮ Counting free subgroups of finite index

Cites Work

• Eine Kennzeichnung der Torusknoten
• On Generalized Free Products of Finite Extensions of Free Groups
• On the Free Product of Two Groups with an Amalgamated Subgroup of Finite Index in each Factor
• The Subgroups of a Free Product of Two Groups with an Amalgamated Subgroup
• Subgroups of HNN Groups and Groups with one Defining Relation
• Generalized Free Products with Amalgamated Subgroups

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