Permutation Groups
This Web page is associated with the book
Permutation Groups, by
Peter J. Cameron, published by
Cambridge University Press
in the
London Mathematical Society
Student Texts series.
Here you will find, in addition to notes and links:
Notes
1. Lewis Nowitz points out that
in Figure 3.3, the cube on the right, which
is used as an aid to explain the concept of antipodal equivalence classes,
is labelled clockwise in bridgesuit order: clubs, diamonds, hearts, and
spades. Therefore, although the cube can't be duplicated, it can
be doubled...
2. As promised, the GAP code in the book has been checked on GAP4 and works
correctly, though the output is not in quite the same form as in the
book; sometimes more or less detail is given. Two new features of GAP4 are
worth pointing out. There is now a command AutomorphismGroup
which can be applied to either a group or a graph, and a command
Transitivity which gives the degree of transitivity of a
permutation group. I have used these in the commented GAP code for
Chapter 3.
3. The reference to the classification of the affine 2transitive groups
(p.110) is inadequate and should be supplemented with the following papers:
 Cristoph Hering,
Transitive linear groups and linear groups which contain irreducible subgroups
of prime order. II.
J. Algebra 93 (1985), 151164.
 Martin W. Liebeck,
The affine permutation groups of rank three,
Proc. London Math. Soc. (3) 54 (1987), 477516.
4. Reviews:
From the review by W. Knapp in Zentralblatt für Mathematik:
... an excellent concise account of the modern theory of permutation groups
including many recent developments...
In spirit and scope it may be considered as a (post)modern equivalent of
H. Wielandt's famous book
"Finite Permutation Groups" ...
A special feature is given by the worked examples using
the computer algebra system GAP.
From the review in the EMS Newsletter:
Students should find this book very stimulating because of the many different
connections it mentions ...
Links
Instructions for Brouwer's DRG finder
The Subject of your mail must be
exec drg
The body of the mail should contain any number of lines of the form
drg d=D B[0],B[1],...,B[d1]:C[1],...,C[d]
where D is the diameter and B[i], C[i] the standard parameters.
References [9], [12], [48], [81], [119], [131] and [165] have all appeared:
[9] László Babai and Peter J. Cameron,
Automorphisms and enumeration of switching classes of tournaments,
Electronic J. Combinatorics 7 (2000), #38 (25pp.)
[12] R. A. Bailey, Association Schemes: Designed Experiments, Algebra and
Combinatorics, Cambridge Studies in Advanced Mathematics, Cambridge
University Press, 2004.
[48] Peter J. Cameron and Csaba Szabó, Independence algebras,
J. London Math. Soc. (2) 61 (2000), 321334.
[81] L. A. Goldberg and M. R. Jerrum, The "Burnside process' converges slowly,
in: Proceedings of Random 1998, Randomisation and Approximation Techniques
in Computer Science, Lecture Notes in Computer Science 1518,
SpringerVerlag, pp. 331345.
[119] Martin W. Liebeck and Aner Shalev, Simple groups, permutation groups,
and probability, J. Amer. Math. Soc. 12 (1999), 497520.
[131] Dugald Macpherson, Sharply multiply homogeneous permutation groups,
and rational scale types, Forum Math. 8 (1996), 501507.
[165] Ákos Seress, Permutation Group Algorithms, Cambridge
Tracts in Mathematics 152, Cambridge University Press, 2003.
Reference [17] is now more accessible; it has been published by
SpringerVerlag as volume 12 in the series Texts and Readings in
Mathematics in 1998.
A proof of the Strong Perfect Graph Conjecture (see p.155) has been
announced by M. Chudnovsky, N. Robertson, P. Seymour and R. Thomas.
Here are some further references:
 P. J. Cameron, Permutations, pp. 205239 in Paul Erdös and his
Mathematics, Vol. II, Bolyai Society Mathematical Studies 11,
Budapest, 2002.

Peter J. Cameron,
Cycle
index, weight enumerator and Tutte polynomial,
Electronic J. Combinatorics
9(1) (2002), #N2 (10pp).

Peter J. Cameron, Michael Giudici, Gareth A. Jones, William M. Kantor,
Mikhail H. Klin, Dragan Marusic and Lewis A. Nowitz,
Transitive permutation groups without semiregular subgroups,
J. London Math. Soc. (2) 66 (2002), 325333.

Peter J. Cameron and C. Y. Ku, Intersecting families of permutations,
Europ. J. Combinatorics 24 (2003), 881890.

Clara Franchi, On permutation groups of finite type,
European J. Combinatorics 22 (2001), 821837.

Daniele A. Gewurz,
Reconstruction of permutation groups from their Parker vectors,
J. Group Theory 3 (2000), 271276.

Michael Giudici, Quasiprimitive groups with no fixed point free elements of
prime order, J. London Math. Soc. (2) 67 (2003), 7384.

Martin W. Liebeck and Aner Shalev, Bases of primitive permutation groups,
pp. 147154 in Groups, Combinatorics and Geometry (ed. A. A. Ivanov,
M. W. Liebeck and J. Saxl), World Scientific, New Jersey, 2003.

A. Maróti, On the orders of primitive groups,
J. Algebra 258 (2002), 631640.
Further references will be added here from time to time.
My homepage
Peter J. Cameron
27 August 2004.