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Contributions to Group Theory
Edited by: Kenneth I. Appel, John G. Ratcliffe, and Paul E. Schupp

Contemporary Mathematics
1984; 517 pp; softcover
Volume: 33
ISBN-10: 0-8218-5035-0
ISBN-13: 978-0-8218-5035-0
List Price: US$74
Member Price: US$59.20
Order Code: CONM/33
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This volume grew out of a desire by the editors to honor their teacher, Roger Lyndon, on the occasion of his sixty-fifth birthday. Five short articles about Lyndon and his contributions to mathematics, as well as twenty-seven invited research papers in combinatorial group theory and closely related areas are contained in this book.

It is a tribute to Lyndon's mathematical breadth that papers covering such a wide array of topics are all closely related to the work he has done. Several of the articles fall into subfields of combinatorial group theory, areas in which much of the initial work was done by Lyndon. Remaining research articles fall into various subfields of homological groups, another area in which he has made major contributions. Research articles, written by some of the leading practitioners in the field, are listed below.

There is a biographical essay about Lyndon by Kenneth Appel, and there are expository articles about his work by Saunders MacLane, John Ratcliffe, Jerome Keisler, and Paul Schupp. MacLane describes the results in Lyndon's doctoral thesis and explains how they fit into the early history of spectral sequences while Ratcliffe presents Lyndon's fundamental work in cohomology of groups in the early part of his career. His work in logic, especially his fundamental results in model theory in the mid 1950s is discussed by Keisler. Lyndon's contribution to group theory over the past twenty years is described by Schupp.

Table of Contents

List of Research Articles
  • S. Andreadakis -- IA-automorphisms of free products of abelian groups
  • K. I. Appel -- On Artin groups and Coxeter groups of large type
  • S. Bachmuth and H. Y. Mochizuki -- The finite generation of \(Aut(G)\), \(G\)-free metabelian of rank \(\geq 4\)
  • J. L. Brenner, R. M. Guralnick, and J. Wiegold -- Two-generator groups III
  • A. M. Brunner, R. G. Burns, and D. Solitar -- The subgroup separability of free products of two free groups with cyclic amalgamation
  • R. G. Burns and T. C. Chau -- Another proof of the Grushko-Neumann-Wagner theorem for free products
  • F. B. Cannonito -- On varietal analogs of Higman's embedding theorem
  • D. J. Collins and H. Zieschang -- On the Whitehead method in free products
  • L. P. Comerford, Jr. and C. C. Edmunds -- Quadratic parametric equations over free groups
  • M. Culler -- Finite groups of outer automorphisms of a free group
  • J. L. Dyer -- A remark on automorphism groups
  • L. Greendlinger and M. Greendlinger -- On three of Lyndon's results about maps
  • K. W. Gruenberg -- On the indecomposability of certain relation cores
  • N. Gupta -- Fox subgroups of free groups II
  • N. Gupta and S. Sidki -- Extension of groups by tree automorphisms
  • A. H. M. Hoare -- Length functions and algorithms in free groups
  • C. Holmes -- Split extensions of abelian groups with identical subgroup structures
  • J. Huebschmann -- Non-planarity of planar groups with reflections
  • R. D. Hurwitz -- A survey of the conjugacy problem
  • B. Jónsson -- Maximal algebras of binary relations
  • R. N. Kalia and G. Rosenberger -- Über untergruppen ebener diskontinuierlicher gruppen
  • A. Karrass, A. Pietrowski, and D. Solitar -- Automorphisms of a free product with an amalgamated subgroup
  • A. Karrass, A. Pietrowski, and D. Solitar -- Some remarks on braid groups
  • K. B. Lee and F. Raymond -- Geometric realization of group extensions by the Seifert construction
  • G. Losey and N. Losey -- The augmentation quotients of the groups of order \(2^4\)
  • A. G. Myasnikov and V. N. Remeslennikov -- Finite-dimensional algebras and \(k\)-groups of finite rank
  • J. G. Ratcliffe -- The cohomology ring of a one-relator group
  • C. L. Tretkoff and M. D. Tretkoff -- Combinatorial group theory, Riemann surfaces and differential equations
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