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Product Code:  CONM/33.E 
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Book DetailsContemporary MathematicsVolume: 33; 1984; 517 ppMSC: Primary 20;
This volume grew out of a desire by the editors to honor their teacher, Roger Lyndon, on the occasion of his sixtyfifth birthday. Five short articles about Lyndon and his contributions to mathematics, as well as twentyseven 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  IAautomorphisms 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  Twogenerator 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 GrushkoNeumannWagner 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  Finitedimensional algebras and $k$groups of finite rank [ MR 767123 ]

John G. Ratcliffe  The cohomology ring of a onerelator group [ MR 767124 ]

C. L. Tretkoff and M. D. Tretkoff  Combinatorial group theory, Riemann surfaces and differential equations [ MR 767125 ]


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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 sixtyfifth birthday. Five short articles about Lyndon and his contributions to mathematics, as well as twentyseven 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  IAautomorphisms 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  Twogenerator 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 GrushkoNeumannWagner 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  Finitedimensional algebras and $k$groups of finite rank [ MR 767123 ]

John G. Ratcliffe  The cohomology ring of a onerelator group [ MR 767124 ]

C. L. Tretkoff and M. D. Tretkoff  Combinatorial group theory, Riemann surfaces and differential equations [ MR 767125 ]