Corrections:

- Page 7, line 13: Not really a mistake but misleading: in place of
"congruent to
*m*mod*p*", read "equal to^{a}*m*". - Page 17, start of 1.13: The number of generators is not necessarily
equal to the number of points! The generators should be
*g*_{1}, …,*g*._{r} - 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*→*g*is a bijection from the^{k/d}*d*th powers to the*k*th powers in*G*, and every*k*th power is a*d*th power, so the two sets are the same. (Spotted by Pablo Spiga.) - Page 50, line −7: χ(
*g*) should be χ(*g*).^{k} - 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 is correct. - Page 63, line −9: should say "subset of Ω
^{2}". (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(3,5
^{2}) should be PΣU(3,5^{2}). (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 Abhyankar.)
- 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.

- Cristoph Hering,
Transitive linear groups and linear groups which contain irreducible subgroups
of prime order. II.
- 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):
*k*should be^{n}*k*^{n-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 "sharply*k*-set-transitive". - 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 Pablo Spiga.)

Updated references:

[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), 321-334.

[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**,
Springer-Verlag, pp. 331-345.

[119] Martin W. Liebeck and Aner Shalev, Simple groups, permutation groups,
and probability, *J. Amer. Math. Soc.* **12** (1999), 497-520.

[131] Dugald Macpherson, Sharply multiply homogeneous permutation groups,
and rational scale types, *Forum Math.* **8** (1996), 501-507.

[165] 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) pjc20(at)st-andrews.ac.uk

Book homepage | Permutation groups resources

Peter J. Cameron

17 January 2016.