TITLE: Lattices with sublattices of a given order
AUTHORS: George Havas and Martin Ward
CITATION:
Journal of Combinatorial Theory 7 (1969) 281-282
ABSTRACT: Birkhoff in his 1948 edition of Lattice Theory poses
the following problem. Given n, what is the smallest integer f(n) such
that every lattice with order r >= f(n) elements contains a sublattice
of exactly n elements? We show that f(n) exists for each n > 0 and
f(n) < n3n for n > 1.
TITLE: Implementation and analysis of the Todd-Coxeter algorithm
AUTHORS: John J. Cannon, Lucien A. Dimino, George Havas and
Jane M. Watson
CITATION: Mathematics of Computation 27 (1973) 463-490
ABSTRACT: A recent form of the Todd-Coxeter algorithm, known as
the lookahead algorithm, is described. The time and space requirements
for this algorithm are shown experimentally to be usually either
equivalent or superior to the Felsch and Haselgrove-Leech-Trotter
algorithms. Some findings from an experimental study of the behaviour
of Todd-Coxeter programs in a variety of situations are given.
TITLE: A Reidemeister-Schreier program
AUTHOR: George Havas
CITATION:
Proceedings of the Second International Conference on the Theory of
Groups, Lecture Notes in Mathematics 372 (1974) 347-356
ABSTRACT: The Reidemeister-Schreier method yields a presentation
for a subgroup H of a group G when H is of finite index in G and G is
finitely presented. This paper describes the implementation and application
of a FORTRAN program which follows this method. The program has been used
satisfactorily for subgroups of index up to several hundred.
TITLE: The two generator restricted Burnside group of exponent five
AUTHORS: George Havas, G.E. Wall and J.W. Wamsley
CITATION:
Bulletin of the Australian Mathematical Society 10 (1974) 459-470
ABSTRACT: The two generator restricted Burnside group of
exponent five is shown to have order 534 and class 12 by two
independent methods. A consistent commutator power presentation for the
group is given.
TITLE: Defining relations for the Held-Higman-Thompson simple group
AUTHORS: John J. Cannon and George Havas
CITATION:
Bulletin of the Australian Mathematical Society 11 (1974) 43-46
ABSTRACT: A set of defining relations for the Held-Higman-Thompson
simple group of order 4 030 387 200 is given.
TITLE: Computational approaches to combinatorial group theory
AUTHOR: George Havas
CITATION:
Bulletin of the Australian Mathematical Society 11 (1974) 475-476
TITLE: Some complexity problems in algebraic computations
AUTHOR: George Havas
CITATION: Proceedings The Complexity of Computational Problem
Solving, University of Queensland Press (1976) 184-192.
TITLE: Computer aided determination of a Fibonacci group
AUTHOR: George Havas
CITATION:
Bulletin of the Australian Mathematical Society 15 (1976) 297-305
ABSTRACT: The Fibonacci group F(2, 7) has been known to be
cyclic of order 29 for about five years. This was first established by
computer coset enumerations which exhibit only the result, without
supporting proofs. The working in a coset enumeration actually contains
proofs of many relations that hold in the group. A hand proof that
F(2, 7) is cyclic of order 29, based on the working in computer coset
enumerations, is presented here.
TITLE: Collection
AUTHORS: George Havas and Tim Nicholson
CITATION:
Proceedings SYMSAC '76, ACM Symposium on Symbolic and
Algebraic Computation, ACM (1976) 9-14
ABSTRACT: Collection processes have been the basis of group
investigations by many people, some using hand calculation, some
machine calculation. We describe a collection process which is
specially efficient in the context of nilpotent quotient algorithm
programs. The principles underlying our collection process are
applicable in general.
TITLE: A computer aided classification of certain groups of
prime power order
AUTHORS: Judith A. Ascione, George Havas and C.R. Leedham-Green
CITATION:
Bulletin of the Australian Mathematical Society 17 (1977) 257-274;
Corrigendum: ibid. 317-319; Microfiche supplement: ibid. 320
ABSTRACT: A classification of two-generator 3-groups of second
maximal class and low order is presented. All such groups with orders up to
38 are described, and in some cases with orders up to
310. The classification is based on computer aided computations.
A description of the computations and their results are presented, together
with an indication of their significance
TITLE: Groups of exponent eight.
AUTHORS: Fritz J. Grunewald, George Havas, J.L. Mennicke and M.F. Newman
CITATION:
Bulletin of the Australian Mathematical Society 20 (1979) 7-16
ABSTRACT: This paper is a survey of the current state of knowledge
on groups of exponent 8. It contains a report on a first stage of an attempt
to answer the Burnside questions for these groups.
TITLE: Integer matrices and abelian groups
AUTHORS: George Havas and Leon S. Sterling
CITATION:
Symbolic and algebraic computation, Lecture Notes in
Computer Science 72 (1979) 431-451
ABSTRACT: Practical methods for computing equivalent forms of
integer matrices are presented. Both heuristic and modular techniques
are used to overcome integer overflow problems and have successfully
handled matrices with hundreds of rows and columns. Applications to
finding the structure of finitely presented abelian groups are
described.
TITLE: The last of the Fibonacci groups.
AUTHORS: George Havas, J.S. Richardson and Leon S. Sterling
CITATION: Proc. Roy. Soc. Edinburgh 83A (1979) 199-203
ABSTRACT: All the Fibonacci groups in the family F(2,n) have
been either fully identified or determined to be infinite, bar one,
namely F(2,9). By using computer-aided techniques it is shown that
F(2,9) has a quotient of order 152x5741, and an explicit
matrix representation for a quotient of order 152x518 is
given. This strongly suggests that F(2,9) is infinite, but no proof of
such a claim is available.
TITLE: Application of computers to questions like those of Burnside
AUTHORS: George Havas and M.F. Newman
CITATION:
Burnside groups, Lecture Notes in Mathematics 806
(1980) 211-230
ABSTRACT: Computers have been used in seeking answers to
questions related to those about periodic groups asked by Burnside in his
influential paper of 1902. A survey is given of results obtained with
the aid of computers and a key program which manipulates presentations
for groups of prime-power order is described.
TITLE: Groups of exponent eight
AUTHORS: Fritz J. Grunewald, George Havas, J.L. Mennicke and M.F. Newman
CITATION:
Burnside groups, Lecture Notes in Mathematics 806
(1980) 49-188
TITLE: Commutators in groups expressed as products of powers
AUTHOR: George Havas
CITATION:
Communications in Algebra 9 (1981) 115-129
ABSTRACT: It is well known that in a free group the simple
commutator [Y, X] (alternatively called the first Engel word) can be
expressed as a product of squares. Likewise the second Engel word
[Y, X, X] can be expressed as a product of cubes. Results on groups of
exponent four imply that the fifth Engel word [Y, X, X, X, X, X] can be
expressed as a product of fourth powers, and explicit expressions have
now been obtained with the assistance of a computer. The results and
the computeraided technique are described.
TITLE: HYPERdisk, an access method for remote disk devices
AUTHOR: George Havas
CITATION: Australian Computer Journal 13 (1981) 64-65
ABSTRACT: A method currently under development for accessing
IBM-compatible disk devices from IBM-compatible is described. The method
is transparent to application programmer and utility user. It for data
transfer over the Network Systems HYPERchannel which is the basis of
the local computer network.
TITLE: The CSIRO HYPERchannel local computer network
AUTHORS: George Havas
CITATION: Proceedings Symposium on Local Area Networks (1982) 5pp.
TITLE: Groups of exponent five and class four
AUTHORS: George Havas and J.S. Richardson
CITATION:
Communications in Algebra 11 (1983) 287-304
ABSTRACT: We investigate presentations for the freest
two-generator group of exponent five and class four, and obtain a
number of minimal presentations, including two which contain the
least possible number of non-fifth-power relators. Our aims are
threefold: firstly, to provide some partial evidence in favour of the
finiteness of the Burnside group of exponent five on two generators;
secondly, to examine a refinement of the well-known question concerning
the existence of minimal presentations for finite p-groups; and
thirdly, to illustrate several ways in which a number of available
computer techniques can be combined to demonstrate the finiteness of a
group with a given presentation.
TITLE: Minimal presentations for finite groups of prime-power order
AUTHORS: George Havas and M.F. Newman
CITATION:
Communications in Algebra 11 (1983) 2267-2275
ABSTRACT: In his survey "Minimal presentations for finite groups"
Wamsley asks: "Are there any four generator five relation
finite groups?" A more precise formulation is: are there any
finite groups which can be generated by 4 elements but not by
3 elements and which can be defined by 5 relations on a
4-element generating set ? The answer is yes. We describe four
such groups and indicate how they were found. The groups are
given in order of increasing size . The proof for the first is
simply a (huge) coset enumeration. The other proofs are more
interesting ; only one is spelt out.
TITLE: Two groups which act on cubic graphs
AUTHORS: George Havas and Edmund F. Robertson
CITATION: Computational group theory, Academic Press (1984) 65-68
TITLE: A Tietze transformation program
AUTHORS: George Havas, P.E. Kenne, J.S. Richardson and E.F. Robertson
CITATION: Computational group theory, Academic Press (1984) 69-73
Zbl. 569.20002 (G. Butler)
ABSTRACT:
A Reidemeister-Schreier program which yields a presentation of a
subgroup H of finite index in a finitely presented group G was described
by Havas [Proceedings of the second international conference on the
theory of groups, Lecture Notes in Math. 372 (1974) 347-356; MR
51#13002]. The program has two stages: first, Schreier generators and
Reidemeister relators for H are computed; then the resulting
presentation is simplified by eliminating redundant generators and by
using a substring searching technique. The Tietze transformation program
which we describe in this paper was originally designed to improve the
simplification stage of that Reidemeister-Schreier program and now also
forms part of the implementation of the modified Todd-Coxeter method [D.
G. Arrell and Robertson, Computational group theory, Academic Press
(1984) 27-32]. The program described here is written in a reasonably
portable superset of FORTRAN 66, and was available at the symposium.
TITLE: Distinguishing eleven crossing knots
AUTHORS: George Havas and L. G. Kovács
CITATION: Computational group theory, Academic Press (1984) 367-373
TITLE: Local Computer Network Systems at CSIRO [In Japanese]
AUTHORS: George Havas and T. Tsukomoto
CITATION: FUJITSU 35 (1984) 107-115.
TITLE: CSIRONET - A national network for computer communication
AUTHORS: George Havas and P.J. Claringbold
CITATION: Proceedings ICCC'84 (1984) 56-63.
TITLE: CSIRONET research and development in Australia
AUTHORS: George Havas and P.J. Claringbold
CITATION: Proceedings World Computing Services Industry Conference IV
(1984) 41-44.
TITLE: User experience with a very high speed local network
AUTHOR: George Havas
CITATION: Proceedings Lancon 84 (1984) 232-237.
TITLE: The connection between the Australian Bibliographic Network
and CSIRONET
AUTHORS: W.S. Ford, George Havas and J.E. Paine
CITATION: Proceedings Second National ABN Conference (1985) 123-128.
TITLE: CSIRONET facilities for industry and government
AUTHORS: George Havas and P.J. Claringbold
CITATION: Proceedings First Pan Pacific Computer Conference (1985)
116, 1494-1515.
TITLE: The integration of diverse technologies by CSIRONET
AUTHOR: George Havas
CITATION: Proceedings VALA Third National Conference on Library
Automation (1985) 37-41.
TITLE: Software product development and export
AUTHORS: George Havas and Howard Kadetz
CITATION: Proceedings ACC '86 (1986) 326-330