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Contributions to Group Theory
 
Front Cover for Contributions to Group Theory
Available Formats:
Electronic ISBN: 978-0-8218-7618-3
Product Code: CONM/33.E
517 pp 
List Price: $74.00
MAA Member Price: $66.60
AMS Member Price: $59.20
Front Cover for Contributions to Group Theory
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Contributions to Group Theory
Available Formats:
Electronic ISBN:  978-0-8218-7618-3
Product Code:  CONM/33.E
517 pp 
List Price: $74.00
MAA Member Price: $66.60
AMS Member Price: $59.20
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 331984
    MSC: Primary 20;

    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 Mac Lane, John Ratcliffe, Jerome Keisler, and Paul Schupp. Mac Lane 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
     
     
    • Articles
    • Kenneth I. Appel - Roger C. Lyndon: a biographical and personal note [ MR 767093 ]
    • Saunders Mac Lane - Spectral complications in cohomology computations [ MR 767094 ]
    • John G. Ratcliffe - Lyndon’s contribution to cohomology of groups [ MR 767095 ]
    • H. Jerome Keisler - Lyndon’s research in mathematical logic [ MR 767096 ]
    • Paul E. Schupp - Some aspects of Lyndon’s work on group theory [ MR 767097 ]
    • S. Andreadakis - IA-automorphisms of free products of abelian groups [ MR 767098 ]
    • Kenneth I. Appel - On Artin groups and Coxeter groups of large type [ MR 767099 ]
    • Seymour Bachmuth and Horace Y. Mochizuki - The finite generation of ${\rm Aut}(G),\ G$ free metabelian of rank $\geq 4$ [ MR 767100 ]
    • J. L. Brenner, R. M. Guralnick and James Wiegold - Two-generator groups. III [ MR 767101 ]
    • A. M. Brunner, R. G. Burns and D. Solitar - The subgroup separability of free products of two free groups with cyclic amalgamation [ MR 767102 ]
    • R. G. Burns and T. C. Chau - Another proof of the Grushko-Neumann-Wagner theorem for free products [ MR 767103 ]
    • Frank B. Cannonito - On varietal analogs of Higman’s embedding theorem [ MR 767104 ]
    • Donald J. Collins and Heiner Zieschang - On the Whitehead method in free products [ MR 767105 ]
    • Leo P. Comerford, Jr. and Charles C. Edmunds - Quadratic parametric equations over free groups [ MR 767106 ]
    • Marc Culler - Finite groups of outer automorphisms of a free group [ MR 767107 ]
    • Joan L. Dyer - A remark on automorphism groups [ MR 767108 ]
    • Leonard Greendlinger and Martin Greendlinger - On three of Lyndon’s results about maps [ MR 767109 ]
    • K. W. Gruenberg - On the indecomposability of certain relation cores [ MR 767110 ]
    • Narain Gupta - Fox subgroups of free groups. II [ MR 767111 ]
    • Narain Gupta and Said Sidki - Extension of groups by tree automorphisms [ MR 767112 ]
    • A. H. M. Hoare - Length functions and algorithms in free groups [ MR 767113 ]
    • Charles Holmes - Split extensions of abelian groups with identical subgroup structures [ MR 767114 ]
    • Johannes Huebschmann - Nonplanarity of planar groups with reflections [ MR 767115 ]
    • R. Daniel Hurwitz - A survey of the conjugacy problem [ MR 767116 ]
    • Bjarni Jónsson - Maximal algebras of binary relations [ MR 767117 ]
    • R. N. Kalia and G. Rosenberger - Über Untergruppen ebener diskontinuierlicher Gruppen [ MR 767118 ]
    • Abe Karrass, Alfred Pietrowski and Donald Solitar - Automorphisms of a free product with an amalgamated subgroup [ MR 767119 ]
    • Abe Karrass, Alfred Pietrowski and Donald Solitar - Some remarks on braid groups [ MR 767120 ]
    • Kyung Bai Lee and Frank Raymond - Geometric realization of group extensions by the Seifert construction [ MR 767121 ]
    • Gerald Losey and Nora Losey - The augmentation quotients of the groups of order $2^4$ [ MR 767122 ]
    • A. G. Myasnikov and V. N. Remeslennikov - Finite-dimensional algebras and $k$-groups of finite rank [ MR 767123 ]
    • John G. Ratcliffe - The cohomology ring of a one-relator group [ MR 767124 ]
    • C. L. Tretkoff and M. D. Tretkoff - Combinatorial group theory, Riemann surfaces and differential equations [ MR 767125 ]
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Volume: 331984
MSC: Primary 20;

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 Mac Lane, John Ratcliffe, Jerome Keisler, and Paul Schupp. Mac Lane 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.

  • Articles
  • Kenneth I. Appel - Roger C. Lyndon: a biographical and personal note [ MR 767093 ]
  • Saunders Mac Lane - Spectral complications in cohomology computations [ MR 767094 ]
  • John G. Ratcliffe - Lyndon’s contribution to cohomology of groups [ MR 767095 ]
  • H. Jerome Keisler - Lyndon’s research in mathematical logic [ MR 767096 ]
  • Paul E. Schupp - Some aspects of Lyndon’s work on group theory [ MR 767097 ]
  • S. Andreadakis - IA-automorphisms of free products of abelian groups [ MR 767098 ]
  • Kenneth I. Appel - On Artin groups and Coxeter groups of large type [ MR 767099 ]
  • Seymour Bachmuth and Horace Y. Mochizuki - The finite generation of ${\rm Aut}(G),\ G$ free metabelian of rank $\geq 4$ [ MR 767100 ]
  • J. L. Brenner, R. M. Guralnick and James Wiegold - Two-generator groups. III [ MR 767101 ]
  • A. M. Brunner, R. G. Burns and D. Solitar - The subgroup separability of free products of two free groups with cyclic amalgamation [ MR 767102 ]
  • R. G. Burns and T. C. Chau - Another proof of the Grushko-Neumann-Wagner theorem for free products [ MR 767103 ]
  • Frank B. Cannonito - On varietal analogs of Higman’s embedding theorem [ MR 767104 ]
  • Donald J. Collins and Heiner Zieschang - On the Whitehead method in free products [ MR 767105 ]
  • Leo P. Comerford, Jr. and Charles C. Edmunds - Quadratic parametric equations over free groups [ MR 767106 ]
  • Marc Culler - Finite groups of outer automorphisms of a free group [ MR 767107 ]
  • Joan L. Dyer - A remark on automorphism groups [ MR 767108 ]
  • Leonard Greendlinger and Martin Greendlinger - On three of Lyndon’s results about maps [ MR 767109 ]
  • K. W. Gruenberg - On the indecomposability of certain relation cores [ MR 767110 ]
  • Narain Gupta - Fox subgroups of free groups. II [ MR 767111 ]
  • Narain Gupta and Said Sidki - Extension of groups by tree automorphisms [ MR 767112 ]
  • A. H. M. Hoare - Length functions and algorithms in free groups [ MR 767113 ]
  • Charles Holmes - Split extensions of abelian groups with identical subgroup structures [ MR 767114 ]
  • Johannes Huebschmann - Nonplanarity of planar groups with reflections [ MR 767115 ]
  • R. Daniel Hurwitz - A survey of the conjugacy problem [ MR 767116 ]
  • Bjarni Jónsson - Maximal algebras of binary relations [ MR 767117 ]
  • R. N. Kalia and G. Rosenberger - Über Untergruppen ebener diskontinuierlicher Gruppen [ MR 767118 ]
  • Abe Karrass, Alfred Pietrowski and Donald Solitar - Automorphisms of a free product with an amalgamated subgroup [ MR 767119 ]
  • Abe Karrass, Alfred Pietrowski and Donald Solitar - Some remarks on braid groups [ MR 767120 ]
  • Kyung Bai Lee and Frank Raymond - Geometric realization of group extensions by the Seifert construction [ MR 767121 ]
  • Gerald Losey and Nora Losey - The augmentation quotients of the groups of order $2^4$ [ MR 767122 ]
  • A. G. Myasnikov and V. N. Remeslennikov - Finite-dimensional algebras and $k$-groups of finite rank [ MR 767123 ]
  • John G. Ratcliffe - The cohomology ring of a one-relator group [ MR 767124 ]
  • C. L. Tretkoff and M. D. Tretkoff - Combinatorial group theory, Riemann surfaces and differential equations [ MR 767125 ]
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