# Contributions to Group Theory

Share this page *Edited by *
*Kenneth I. Appel; John G. Ratcliffe; Paul E. Schupp*

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

## Contributions to Group Theory

- Table of Contents ix10 free
- Preface xi12 free
- Roger C. Lyndon: a Biographical and Personal note 114 free
- Spectral Complications in Cohomology Computations 1124
- Lyndon's Contribution to Cohomology of Groups 2437
- Lyndon's Research in Mathematical Logic 2942
- Some Aspects of Lyndon’s Work on Group Theory 3346
- IA-Automorphisms of Free Products of Abelian Groups 4457
- On Artin Groups and Coxeter Groups of Large Type 5063
- The Finite Generation of Aut(G), G-Free Metabelian of Rank ≥ 4 7992
- Two-Generation Groups III 8295
- The Subgroup Separability of Free Products of Two Free Groups with Cyclic Amalgamation 90103
- Another Proof of the Grushko-Neumann-Wagner Theorem for Free Products 116129
- On Varietal Analogs of higman's Embedding Theorem 134147
- On the Whitehead Method in Free Products 141154
- Quadratic Parametric Equation Over Free Groups 159172
- Finite Groups of Outer Automorphimsms of a Free Group 197210
- A Remark on Automorphism Groups 208221
- On Three of Lyndon's Result About Maps 212225
- On the Indecomposability of Certain Relation Cores 214227
- Fox Subgroups of Free Groups II 223236
- Extension of Groups by Tree Automorphisms 232245
- Length Functions and Algorthims in Free Groups 247260
- Split extensions of Abelian Groups with Identical Subgroup Structures 265278
- Non-Planarity of Planar groups with Reflections 274287
- A Survey of the Conjugacy Problem 278291
- Maximal Algerbars of Binary Relations 299312
- Über Untergruppen Ebener Diskontinuierlicher Gruppen 308321
- Automorphisms of A Free Product with an Amalgamated Subgroup 328341
- Some Remarks on Braid Groups 341354
- Geometric Realization of Goup Extensions by the Seifert Construction 353366
- The Augmentation Quotients of the Groups of Order 24 412425
- Finite-Dimensional Algebras and K-Groups of Finite Rank 436449
- The Cohomology Ring of a One-Relator Group 455468
- Combinatoria Group Theory, Riemann Surfaces and Differential Equations 467480