Groups, trees and projective modules

zbMath0427.20016MaRDI QIDQ1136853

Warren Dicks

Publication date: 1980

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

zbMATH Keywords

projective modulesfree groupsinner derivationGrushko-Neumann theoremBass-Serre theorynormal form theoremaugmentation idealgroup pairsfundamental group of a connected graph of groupsgroups of cohomological dimension onegroups operating on treesprojective right module

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) General structure theorems for groups (20E34) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Homological methods in group theory (20J05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

Related Items (37)

Embedding arbitrary algebras in groups ⋮ Deformation spaces of trees. ⋮ Splittings of Poincaré duality groups ⋮ Fixed subgroups of automorphisms of free by finite groups: an extension of Cooper's proof ⋮ Graph products of groups and group spaces ⋮ On Splitting Augmentation Ideals ⋮ Unnamed Item ⋮ Qurves and quivers ⋮ On the forcing relation for surface homeomorphisms ⋮ Actions of finite groups of graphs and related automorphisms of free groups ⋮ On the Rationalization of the Circle ⋮ Virtually free pro-\(p\) groups. ⋮ Automorphism groups of hyperbolic lattices ⋮ Semistability of cubulated groups ⋮ Genus for groups. ⋮ Virtually free groups and integral representations ⋮ On locally indicable groups ⋮ Dynamical correspondences of \(L^2\)-Betti numbers ⋮ Quasi-Projective and Relative Cohomological Dimension of Groups ⋮ CONTEXT-FREE GROUPS AND THEIR STRUCTURE TREES ⋮ Relative ends and duality groups ⋮ Profinite properties of graph manifolds ⋮ Profinite detection of 3-manifold decompositions ⋮ THE FIGURE EIGHT KNOT GROUP IS CONJUGACY SEPARABLE ⋮ Cutting up graphs ⋮ Hereditary semigroup algebras ⋮ Automorhisms of enveloping algebras ⋮ A descent principle in modular subgroup arithmetic. ⋮ Modules ⋮ Intersections of finitely generated subgroups of free groups and resolutions of graphs ⋮ Cyclic extensions of free pro-\(p\) groups ⋮ Theory of groups that act on trees ⋮ The accessibility of finitely presented groups ⋮ Amalgams of prime index ⋮ Integral group rings: Groups of units and classical K-theory ⋮ Dual Cones and the Voronoi Algorithm ⋮ Algebraic 𝐾-theory of poly-(finite or cyclic) groups

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