# Errata for “Adventures in Group Theory”, 2nd edition

Compiled by Haruyuki Kawabe and others
(see below for acknowledgements).

Note: Rubik’s cube moves displayed by Sage (using rubik.plot_cube) are not the same as the book. For example, the Rubik’s cube move R is displayed in 2d using rubik.display2d("R") as the move R-1. However, the color plots rubik.plot_cube("R") (in 2d) and rubik.plot3d_cube("R") (in 3d) are consistent with the book’s notation.

chapter page line read should be
1 3 -5 im in
3 -7 _\wedge (i.e., _∧ ) _\vee (i.e., _∨ )
5 8 De
Morgans’s Law
distribution law
5 11 laws of negation De Morgan’s laws
7 1 [Gar1] (SEE REMARK 1)
11 -12 two four
2 13 2 And Can
13 3 And Can
16 -12 or of
19 -2 vertices vertices,
edges
19 -1 f_1 f_0, f_1
23 6 left matrix (SEE REMARK 2)
23 3 diagonal triangular
23 7 of or
27 6 S a set
33 7 5 jars 3 jars
33 -17 n-m n-m+1
34 13 n |’s n-1 |’s
3 46 16 1 3 2 1 4 3 2 1
56 -5 (b_1, n) (b_{n-1}, n)
56 -5 (b_2, n) (b_{n-2}, n)
56 -5 (b_3, n) (b_{n-3}, n)
56 -5 (b_{n-1}, n) (b_1, n)
bells
bells.
59 -16 the next a later
4 63
 * U * * L * R * * D * * * * * *

 * u * * l * r * * d * * * * * *
63 -9 five four
64 -11 five four
66 7 matrix array
66 -5 f_1r_1 f_1
70 -2 2×2 2x2x2
80 2 [B1] [Bur]
81 10 [f_1.f_5.f_6] [f_2.f_1.f_6]
86 -1 denote and $\ell_4$ denote
5 89 1 that there there
96 -13 S_{54} S_{48}
99 -5 S_4 S_{48}
104 2 S_{54} S_{48}
107 -7 2*t^6+2*t^3+7*t^2+t t^6+t^3+3t^2+t
110 6 Feynmann Feynman
116 -3 for all x beloinging to X (SIMPLY REMOVE)
117 -6 H |H|
118 17 lemma proposition
6 124 -15 (sometimes called the toggle vector) (SIMPLY REMOVE)
129 -11 E_{22} E_{2,2}
130 5 M_{N} M_{N\times N}
132 -2 \vec{v_i} \vec{f_i}
134 19 if of
135 12 theory theorem
138 -14 1,12 12
138 -13 2,9 9
138 -12 3,10 10
138 -11 4,11 11
138 -10 5,7 7
138 -9 6,8 8
138 -8 5
138 -7 6
138 -6 2
138 -5 3
138 -4 4
138 -3 1
7 148 9 digraph graph
148 14 3×3 3x3x3
148 -2 I was I was born
153 9 1307674368000 653837184000
8 158 17 remove “,” after cos(\theta)
159 3 lemma theorem
163 2 number number perfect
9 169 -2 sgn sign
174 20 f \phi
178 -14 g_1\cdot g_2^(-1)=e_2 g_1\cdot g_2^{-1}=e_1
182 -1 f(G_1) f(G_2)
187 -5 C V
191 9 a+b+c\equiv 0 a+b+c
195 -13 missing commas after x_1 and after y_1
197 12 diag(v) (SEE REMARK 3)
197 13 (3,3) entry of the 2nd matrix should be 1 instead of -1
10 201 -11 transpositions the generators
217 2 n+1 n
217 10, 18 h_j h_i
11 222 1 v(g) vec{v}(g)
223 -14,-15 H H’
226 -3 (r,s,0,0) (r,0,s,0)
228 -16 v_k v_{k+1}
229 -1,-2 \equiv \cong
231 -1 10^6 10^7
241 8 plane line
12 242 9 (SEE REMARK 4)
242 15 (SEE REMARK 4)
244 14 plane line
245 -9 F_5^X (SEE REMARK 5)
245 -10,-12 F_F F_5
246 3 elementary transvections (SEE REMARK 6)
249 15,17,19 P^1(F) P^1(F_7)
13 252 15 f_V f_V:G\to S_v, g \mapsto g_V
(SEE REMARK 7)
253 4 f_{EV} f_{VE}
255 -15 to -13 vague statement of Claim 1 a more precise meaningful statement
257 -20 S_V x C_3^8 C_3^8 x S_V
257 -16 p(g)\vec{v}(h) p(g)^{-1}\vec{v}(h)
260 -10 Corner Edge
261 -5 r \in S_V, (simply remove)
263 -1 5.10 4.4 (but no edge-labels are given)
14 270 7 the pile is the stack of cards is
273 14 M_12 |M_12|
274 8 F; F:
278 8 A_24 A_{24}
279 9, 10 weights of the weight distribution of the
279 9 [n, k, d] where n is the length, k is the dimension, and d is the minimum distance

(SEE REMARK 8)

280 -11 12.3 12.4
283 2 mthods methods
283 12 left right
15 285 4 Abyss the Abyss
286 17 face corners
288 -5, -4 G_{k+1}/G_k G_k/G_{k+1}
288 -3 m_{n-1} r_{n-1}
288 -2 n_1 r_1
289 1 g_{k+1,j}G_k g_{k+1,j}G_{k+1}
289 2 n_1 r_k
292 16 (1,2) (2,1)
292 18 (4,2) (2,4)
294 -16 [FRU \cdot
FLU]^3
(FRU \cdot
FLU)^3
294 -12 [FRU \cdot
BLU]^5
(FRU \cdot
BLU)^5
295 12 bottom bottom and
left center facets
295 -2 UL $UL$
298 -5 9.4 10.4
Bibliography 299 missing reference [Bur] R. Burn, Groups: a path to geometry, Cambridge Univ. Press, 1985.
299 missing reference [Gar3] M. Gardner, Eight problems, in New Mathematical Diversions, M.A.A, 1995.
301 -18 group groups
REMARK 1: The problem is
described in [Gar3], “New
Mathematical
Diversions”
REMARK 2: 3×4 matrix would also be appropriate
for the example.
REMARK 3: The function diag is not
defined.
(It defines a diagonal matrix with the given entries on the diagonal.)
REMARK 4: The matrices on
right hand side of
the equation should be swapped.
REMARK 5: F_5^X is not defined.
REMARK 6: The term is not explained in
this book. See transvection on Wikipedia, for example.
REMARK 7: f_V is defined to be the map F_V(g)=g_V.
REMARK 8: the notation is not defined.

The typo mentioned above on page 46 was caught by Greg Ives – thank you!
The typos mentioned above on pages 107, 153 were caught by Matthias Rudnick, who also noticed the Sage bug in display2d – thank you!
The typo mentioned above on page 231 was caught by Michael Burns – thank you!
The errata mentioned above on page 255 (the statement of Claim 1 is so vague it has no
meaningful mathematical content) was caught by Prof. Juergen Voigt – thank you!
I think Haruyuki Kawabe for the remaining typos, as well as his Japanese translation of the book.