Errata and Comments Page for 1st printing of Adventures in group theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys

Errata which have been fixed in the 2nd printing are marked with a *. To the best of my knowledge, all errata are fixed in the 2nd edition.
News: The 2nd edition is now available at amazon.com or from the Johns Hopkins University Press. (All royalties go directly to charity - half to the Sage Foundation to support open-source mathematical software development, and half to the Earth Island Institute, an environmental organization with projects all over the world.)

Thanks to those readers who emailed or snail-mailed me some of the following errata. In particular, I'd like to thank Jamie Adams, Lewis Nowitz, David Youd, Roger Johnson, Jaap Scherphuis, Michael Hoy, Tom Davis, John Rood, Trevor Irwin, Stephen Lepp, Mark Edwards, Carl Patterson, Peter Neumann (seven pages!), Bill Zeno, Herbert Kociemba, Alastair Farrugia, Matthew Lewis, and Christopher Tuffley.

General comments:

page, line
read
should be
ix, 8 the previous a previous
xiii, -8 solved was motivated by
6, -6 not a subset of a finite set not finite
6, -1 it's its
14, 11 fg fog = fg
14, -6 |S| = |T|. |S| = |T| < infinity..
15, 8 f:S --> Z f:Z-->S
16, -9,-8 linear transformations matrices
19, -11 k = m k = m+1
19, -11 a_{ij} (AB)_{ij}
19, -9 row of column of
20, -1 det(Aij) det(Aij)aij
21, 2 or and
22, -3 21 23
22, -18 (s,t) belongs to S (s,t) belongs to R
*26, 19 Exactly one Each one
*26, 20 30 103=1000
*26, -9 and an
*26, -3 an and
27, 12 object objects
27, -12 n, n-1, ..., n-m n, n-1, ..., n-m+1
27, -10 poker hands "ordered poker hands"
27, -8 52*51*50*49*48*47 = 14658134400 = (1.4...)x1010 52*51*50*49*48 = 311875200 = (3.1...)x108
28, 5 an combination a combination
28, 13-14 right ... left left ... right
31, 15 Ss Sc
33, -13 a point of points a collection of points
33, -6 It's Its
37, 10 chapter 8 chapter 9 (see Theorem 9.3.1)
37, 15 then are distinct then
38, 15 Si Ai
43, -18 (n,an) (n,an-1)
42, 9-10 row column
43, -14 (bn,n) (bn-1,n)
*45, 23 a(ab)2 (ab)2a
*45, 26 a(ab)2 (ab)2a
*46, 5 ka(ab)2 k(ab)2a
*46, 7 k2a(ab)2 k2(ab)2a
47, -1 five four
50, -10 radians (degrees)
51, 2 closed geodesic path closed path
*52, -9 f1 f1r1
*61, 18 120 degrees 72 degrees
67, 1 {i,j,k}. {i,j,k}, and x doesn't equal y.
68, -9 D2n Dn
70, -5 o : G x G x G G x G ---> G
72, -9 What didn't Why didn't
76, 16 such that and a place token p_{i+1} such that
*76, -3 {1,3,6} {1,3,4}
*76, -2 {3,6} {3,4}
77, -2 (Lagrange) ("Lagrange's Theorem")
78, 7 x in G. x in G. (Exercise: verify this.)
78, 8 "so" "(see Ponderable 2.3.3), so"
*78, -9 "...belongs to G" "...belongs to Z(G)"
79, 13 identifies identified
79, -4 likelyhood likelihood
*80, 4 MD2 MF2
*80, -6 ...showed to there ... ...showed that there ...
*82, top diagram label "8" (resp., "6") on cube label "6" (resp., "8") on cube
84, -14 ... substitutions ... des substitutions
84, -3 gh=1 gh=g
86, 5 g in G_* d \geq 0
*87, 2 clases classes
*87, 10-11 g*x*g^{-1} g*y*g^{-1}
88, -10 left action right action
88, -5 right left
88, -3 on the right on the left
89, 5 right action left action
89, 15 send sent
89, 18 are induce
89, 19 (though not all are)! .
89, 21 In other words, Roughly speaking,
89, 21-22 group acting on a set at `random' `random` finite group acting primitively on a finite set
89, 24 corners corner
89, -1, -2 (a), (b) (b), (c)
91, 18 set of consisting set consisting
*92, -6 right face down face
93, 17 sbgroup subgroup
93, lines 24,25 groups subgroups
94, 15 both and both an
95, 8-9 Then ... G = H* ... maximal). Thus p either ... Then G = H* ... maximal). This implies p either ...
95, 10 In either case, the result ... hypothesis. The result ... hypothesis.
95, 13 (Lagrange) ("Lagrange's Theorem")
*96, 13 a(ab)2 (ab)2a
99, 8 organisational organizational
99, -13 choosen chosen
99, -11 always be ... is), be ... is) is 1,
*99, -7 .5 1
99, -7 always be
99, -6 always be solved. be solved is 1.
100, 18 and shall and
*101, 14 (M-1)(N-1) N(M-1)+M(N-1)
*101, section 6.3.1 Merlin's magic 3x3 light's out
104, 5 for some provided
*104, 7 Ei,j in MN Ei,j in MMxN
*105, -8 omit "Merlin's magic and"
105, 3 2 3
105, 4 3 4
105, 5 4 5
106, -7 = 0 \not= 0
107, -20 effectivly effectively
107, -14 intorduce introduce
107, -9 \cdot F \cdot : F
107, -4,-3 the vector \vec{0}=(0,0,...,0)\in V satisfies there is a vector \vec{0}\in V satisfying
109, 15 if multiplicity of multiplicity
109, -16 matrix square diagonalizable matrix
110, 17 is upper-triangular. The number of non-zero entries on the diagonal is reduced. The number of non-zero rows
111, -2 reculangular rectangular
111, -1 Aien Alien
*112, figure 6.5.5 The outer pentagon (numbers 7-11) should be rotated clockwise 36 degrees with respect to the rest.
*114, 10 matrix T see above
*114, -5 15 16
*114, -3 is 1 is 0
*114, -2 are initial are no initial
116, 11 eminating emanating
117, 8 who whom
117, 9 laywer lawyer
117, -6 v's v
*117, -2 (1 2) , (2 3) (1,2) , (2,3)
119, -21 Micheal Michael
120, -12 who whom
122, 6 We can ... path p, Let a path p on puz(Gamma) to be a sequence of moves
122, 7 n <= 1 n >= 1
122, 14 of paths based of closed paths based
*122, 12 14-15 puzzle 15 puzzle
123, 1 has has at most
125, 9 vertices edges
126, line -7,-6,-5 symmetric symmetry
127, -12 (1/2)(...||^2 + ||.. (1/4)(...||^2 - ||..
127, -1 transpose identity. transpose
128, 9 *B *A
128, 10 if an if and
129, 3-4 In particular, ... invertible. The matrix A is invertible since, by definition, its inverse is ^tA.
132, 8 permutations of permutations in
132, 17 permutations of permutations in
132, 17 A5 x S5 A5 x C2
138, 1 E. Jordan C. Jordan
139, 12 X x X X x X - Delta (where Delta = {(x,x) | x in X})
139, 17 belonging to X belonging to X, xi <> xj
139, 17 for each provided
139, -15 group permutation group
139, -11 [R] [DiMo], Theorem 7.6A
141, lines 4,5 , and in ... i,j,k. , as in section 5.1.
*141, 20,21 left, right right, left (resp.)
*141, 23 Let g Let x
141, -8 concept concepts
141, lines -7, -6 finite groups finite simple groups
142, 9 three cubes two cubes
142, -14 for all 1 <= i <= n provided 1 <= i <= n
142, -1 for all 1 <= j <= n provided 1 <= j <= n
143, 2 <= 1 <= n
145, 4 E. Galois Ruffini and Abel
146, 11 who whom
146, -15 normal groups normal subgroups
147, -21 isomomorphism isomorphism
147, -1 isomorphism between isomorphism
150, -14 H acts on X. Note Note, H acts on X and
150, -4 is an element are elements
150, -3 any element other element of E each other
*156, 3 somwhat somewhat
*156, -1 H1 x H2 H1 xphi H2
157, -19 colun column
158, -2,-1 (x,y) g
158, -1 (-x,-y) -g
161, 10 group arose group, originally arose
*163, -14 n n-1
*163, -12 n=2 n=3
164, 15 Rubik's cube. Rubik's cube which does not contain a basic move followed by its inverse
165, 9 , however . However,
165, 18 occurance occurence,
165, -10 cardiality cardinality
166, -10 who whom
166, -6 R The letter script-R
166, -5 realtions relations
166, -3 relations R relations script-R
*170, 4-5 should be a horizonal line separating cases 15,16
172, -13 (a) .
172, -11,-10 , and in ... {i,j,k}. , as in section 5.1.
*178, 1 lu, and bu lu, bl, and bu
*180, 3, 4, 7, 8 corner edge
*180, 4 vertex edge
*180, 5 vertices edges
*180, 17 (0,1,0,0,0,1,1,0,0,1,0,0) (0,1,0,0,0,0,0,0,0,1,0,0)
180, -1 (SV wr C38)x(SE wr C212) (C3 wrSV )x(C2 wr SE)
181, 1-2 C38xSVx C38xSV C38xSVx C212xSE
185, 12-13 allows us to count its elements easier. enables us to determine the size of this group.
186, -1 isomomorphism isomorphism
188, -2 of (non-trivial) of
189, 9 haiku poem
193, 8 x1e1 +...xn en x1e1 +...+xn en
194, 15 More generally, let Let
194, lines 21, -10 e2i-2 e2i-1
195, 6 < F,U > .... < sigma(F),sigma(U) > isom S7, < rho(F),rho(U) > isom PGL2(F5),
198, -6 fractions fractional
201, 3 enties entries
201, lines -12, -14, -16 polyhedra polyhedron
205, 7 undeground underground
215, -13 SE wr C2 C2 wr SE
216, -2 G G_1
216, -2 G G_1
217, 1 and 4 G G_1
217, 14-16 Theorem 13.5.1 see above
217, 18 possible possible in G
217, -9 up down
223, -15 isocahedron icosahedron
224, -13 in his PhD thesis. a year after his Docteur es Sciences thesis in 1859.
225, -18 stating containing
225, -11 A8, A12 A7, A11
229, -8 Matheiu Mathieu
230, lines -18,-17,-7 isocahedron icosahedron
230, -14 many experts thought they had classified all finite simple groups some experts thought all finite simple groups had been classified
231, lines 7,8,11 parallelpiped parallelepiped
231, 20 giving the first proof giving one of the first proofs
232, -1 [R], ch. 9 [DM], Theorem 7.6A
251, -11 Berlekamp E. Berlekamp
*253, 17 D. Hofstatler D. Hofstater
*253, 17 Metamathematical Themas Metamagical Themas
259, 14 E. Jordan C. Jordan

Last Updated on 2009-6-8

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