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TitleEssays in Group Theory [electronic resource] / edited by S. M. Gersten
ImprintNew York, NY : Springer New York, 1987
Connect tohttp://dx.doi.org/10.1007/978-1-4613-9586-7
Descript VII, 342p. 46 illus. online resource

SUMMARY

Essays in Group Theory contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Special mention should be given to Gromovs̀ paper, one of the most significant in the field in the last decade. It develops the theory of hyperbolic groups to include a version of small cancellation theory sufficiently powerful to recover deep results of Ol'shanskii and Rips. Each of the remaining papers, by Baumslag and Shalen, Gersten, Shalen, and Stallings contains gems. For example, the reader will delight in Stallings' explicit construction of free actions of orientable surface groups on R-trees. Gersten's paper lays the foundations for a theory of equations over groups and contains a very quick solution to conjugacy problem for a class of hyperbolic groups. Shalen's article reviews the rapidly expanding theory of group actions on R-trees and the Baumslag-Shalen article uses modular representation theory to establish properties of presentations whose relators are pth-powers


CONTENT

Affine Algebraic Sets and Some Infinite Finitely Presented Groups -- Reducible Diagrams and Equations Over Groups -- Hyperbolic Groups -- Dendrology of Groups: An Introduction -- Adian Groups and Pregroups


Mathematics Group theory Mathematics Group Theory and Generalizations



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