COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

vi Contents
E. KRAUSE and K. WESTON: An algorithm related to the restricted
Burnside group of prime exponent 185
A. L. TRITTER: A module-theoretic computation related to the Burnside
problem
J. J. CANNON: Some combinatorial and symbol manipulation pro-
189 Foreword
grams in group theory 199
IF the electronic digital computer has not already virtually taken over the
P. G. RUUD and R. -OWN: The computation of irreducible representations
of finite groups of order 2”, n e 6 205
world’s arithmetic it will have done so before long. This remarkable
success story in the field of applied mathematics-much of it very simple
N. S. MENDELSOHN: Some examples of man-machine interaction in
the solution of mathematical problems
R. J. PLEMMONS: Construction and analysis of non-equivalent finite
semigroups
217
223
mathematics, admittedly, such as cost calculations-contrasts strongly
with the machine’s very moderate impact so far on pure mathematics.
Obvious economic considerations account for much of this difference:
no one can be surprised that the need to optimize the design of a nuclear
power reactor or to develop a stores holding and purchasing strategy for a
T. TAMURA: Some contributions of computation to semigroups and
groupoids
D. E. KNUTH and P. B. BENDIX: Simple word problems in universal
algebras
229
263
large factory provides more economic drive than, say, the properties of the
partition function. But this can hardly apply in a university environment,
where the pure mathematicians have as much right to the central computing
service as anyone else. The explanation must be the great difficulty of
the problems; the machine offers great powers of logical processing, of
L. J. PAIGB: The application of computers to research in non-associative
algebras 299
which arithmetic is only a small and not very interesting part, but it is far
from clear how these can be used in the service of anything that can be
called genuine mathematics.
C. M. GLENN~E: Identities in Jordan algebras 307
A. D. KEEDWELL: On property D neofields and some problems concerning
orthogonal latin squares 3 1 5
However, work has in fact been going on in various fields of pure
mathematics ever since computers became available. Professor Douglas
Munn, surveying the scene from the point of view of an algebraist, decided
in 1966 that enough had been done on the application of computers to
J. W. P. HIRSCHFELD: A projective configuration
W. D. MAURER: The uses of computers in Galois theory
321
325
abstract algebra to warrant the holding of an international conference,
to assess what had been achieved and to identify promising lines of future
research. A frequent visitor to the Atlas Laboratory, he talked about this
with me and my colleague Dr. Robert Churchhouse, and after very little
discussion we found ourselves agreeing that the time was indeed right for
such a conference, that Oxford would be an admirable location and that
the Atlas Laboratory should organize it. We approached Professor Graham
Higman who immediately and enthusiastically agreed to give his support;
and with equal immediacy and enthusiasm had Professor Coulson’s
permission to hold the conference in Oxford’s beautiful new Mathematics
Institute.
The success of the meeting must be judged from the quality of the papers,
reproduced in this volume. I want to record my gratitude to the Science
Research Council, who allowed me to meet some of the expenses from
Atlas Laboratory funds, and to I.C.T. Limited for generous financial
support: jointly, they made it possible to hold the conference. The staff
of the Mathematics Institute were as helpful and welcoming as anyone
vii
J. H. CONWAY: An enumeration of knots and links, and some of their
algebraic properties 329
H. F. TROTTER: Computations in knot theory 359
S. LIN: Computer experiments on sequences which form integral
bases 365
H. COHN: Application of computer to algebraic topology on some
bicomplex manifolds 371
H. ZASSENHAUS: A real root calculus 383
R. E. QLMAN : Some computational problems and methods related to
invariant factors and control theory 393
List of participants 399