This volume grew out of the conference “Decision Problems in
Group Theory”, (CODEP) held at the University of California, Irvine,
in September 1969, with the support of the United States National
Science Foundation, the Army Research Office, Durham, and the
Air Force Office of Scientific Research (Air Force Systems Command).
These same organizations supported the preparation of this
volume.
Althoughcutthg broadly across logic, group theory and other
fields of algebra, topology and computer science, the mathematics
discussed in the conference and this book has, we would argue, an
inherent unity of purpose and method. The unifying aspects are
the common concern with algorithms and the common use of a
certain kind of combinatorial analysis. This analysis had been used
in logic for a long time, particularly in the study of proofs, before
it then spread - in the very development of the field we are here
presenting - to the study of “word problems” in groups and semigroups.
To us it seems unlikely that the argument of Novikov and
Adjan for the Burnside Problem, published in 1968 and whose
central ideas are explained in the present volume, or the argument
of Britton for the same result in the present volume, could have
been discovered by a “pure” group theorist!