Permutation Groups: Misprints, Corrections, Improvements
- Page 7, line 13: Not really a mistake but misleading: in place of
"congruent to m mod pa", read "equal to m".
- Page 17, start of 1.13: The number of generators is not necessarily
equal to the number of points! The generators should be g1,
- p.21, l.9: "Turrull" should be "Turull". (Spotted by P. P. Pálfy)
- Page 30, Exercise 1.19(b): The congruence q≡1 (mod 4) should be replaced by q≡−1 (mod 4). Also, the assumptions of the exercise are stronger than needed. I am grateful to Dávid Szabó for this, and with his permission I have posted his amendment and solution here.
- Page 30, Exercise 1.21: the question should say "of degree greater
than 5". Note that it applies to finite and infinite permutation groups.
(Spotted by Alice Devillers.)
- Page 32, Exercise 1.30(b): "… fixed point set of K" (not
G). (Spotted by Pablo Spiga.)
- Page 34, Exercise 1.36: for the "if" part of the question, you must
assume that G is a transitive permutation group – this follows from
the sharp transitivity of S when you are going in the "only if"
direction. (Spotted by Pablo Spiga.)
- Page 50, line 12: this is not very clear.
The map g → gk/d
is a bijection from the dth powers to the kth powers in G,
and every kth power is a dth power, so the two sets are the
same. (Spotted by Pablo Spiga.)
- Page 50, line −7: χ(g) should be
- Pages 54,55: The inner product of π(n−2,1,1)
with itself should be 7, not 6 (in two places). The conclusion of the argument
- Page 63, line −9: should say "subset of Ω2".
(Spotted by Robin Whitty.)
- Page 76, line 2: g(θ)=1, g(φ)=0 (not f).
- Page 77, line 2: +(k−mu) should be −(k−mu).
(Spotted by P. P. Pálfy)
- Page 83, line 4: PΣL(3,52) should be
PΣU(3,52). (Spotted by P. P. Pálfy)
- Page 101, 2nd line of proof of 4.3: G should be N.
(Spotted by Nick Cavenagh.)
- Page 101: a more elementary argument to finish the proof of
Theorem 4.3 is given here. (Spotted by Ram
- The reference to the classification of the affine 2-transitive 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), 151–164.
- Martin W. Liebeck,
The affine permutation groups of rank three,
Proc. London Math. Soc. (3) 54 (1987), 477–516.
- Pages 135-138, Section 5.3: In the discussion of first-order logic,
I neglected to say that the binary relation = is assumed to be among
the logical symbols, and we always assume that its interpretation is the
usual one of identity.
- Page 139, Section 5.5, line 5: delete "countable". (Spotted by
P. P. Pálfy)
- Page 164, Exercise 5.23(b): kn should be
kn-1. (Spotted by Nathan W. Lemons)
- Page 166, line 14: it should read "is reflexive and transitive".
(Spotted by Pablo Spiga)
- Page 166, last line: "cofinitary" should be "finitary". (Spotted by
P. P. Pálfy)
- Page 170, line 6: For "sharply k-transitive" read
- Page 180, line 21: B a maximal block meeting Δ. (Spotted by
P. P. Pálfy)
- Page 188, line 9: delete the words "of the same order".
- Page 194, line 3: delete p.
- Page 198, Exercise 7.4: should say "Table 7.4" (not "Table 6.4").
(Spotted by Alberto Basile.)
- Page 200, Reference 15: Aron Bereczky's paper is in the Bulletin
of the London Mathematical Society, not the Journal. (Spotted by
 László Babai and Peter J. Cameron,
Automorphisms and enumeration of switching classes of tournaments,
Electronic J. Combinatorics 7 (2000), #38 (25pp.)
 R. A. Bailey, Association Schemes: Designed Experiments, Algebra and
Combinatorics, Cambridge Studies in Advanced Mathematics, Cambridge
University Press, 2004.
 Peter J. Cameron and Csaba Szabó, Independence algebras,
J. London Math. Soc. (2) 61 (2000), 321-334.
 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,
Springer-Verlag, pp. 331-345.
 Martin W. Liebeck and Aner Shalev, Simple groups, permutation groups,
and probability, J. Amer. Math. Soc. 12 (1999), 497-520.
 Dugald Macpherson, Sharply multiply homogeneous permutation groups,
and rational scale types, Forum Math. 8 (1996), 501-507.
 Ákos Seress, Permutation Group Algorithms, Cambridge
Tracts in Mathematics 152, Cambridge University Press, 2003.
Please email corrections to me: p.j.cameron(at)qmul.ac.uk or (preferred)
Permutation groups resources
Peter J. Cameron
17 January 2016.