# 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 15 -8 T \subset \mathbf{R} 0 \in T\subset \mathbf{R} 16 -12 or of 18 5 f^{-1}(s) f(s) 18 8 f\circ g = fg g\circ f = gf 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 26 7 +(1,1,1) / +2(1,1,1) +3(1,1,1) / +6(1,1,1) 27 6 S a set 32 -9 S_1\times S_n S_1\times \dots \times S_n 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 50 -3 O_1’\to O_j’ O_j’\to O_j’ 53 Fig. U/D/L/R/B/F u/d/l/r/b/f 53 -4 (a_1,a_k)…(a_1,a_2) (a_1,a_2)…(a_1,a_k) 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) 56 -4 to -9 in alg. step 4 omitting 4th, 6th, 7th sentences gives a simpler way of describing this step 57 -6 adjacent. bells adjacent bells. 59 -16 the next a later 4 63 12 U/L/D/R u/l/d/r 63 -9 five four 64 -11 five four 66 7 matrix array 66 -5 f_1r_1 f_1 67 -8 (11,22)(12,23)(13,24) (11,20)(12,19)(13,18) 70 -2 2×2 2x2x2 78 10 4.6 4.5 80 2 [B1] [Bur] 81 10 [f_1.f_5.f_6] [f_2.f_1.f_6] 86 -12 rotations rotation 86 -1 denote and $\ell_4$ denote 5 89 1 that there there 91 12 omit “necessarily” 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 115 11 in Hg in gH 116 -15 set X. set X on the left. 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} 131 -10 superdiagonal of 1’s in Bn(x) superdiagonal of -1’s in Bn(x) 132 -2 \vec{v_i} \vec{f_i} 134 19 if of 135 12 theory theorem 137 -7 editition edition 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 7 145 11 label vertices of graph on LHS as a,b,c (clockwise) label vertices of graph on RHS as a,c,b (clockwise) 148 9 digraph graph 148 14 3×3 3x3x3 148 -2 I was I was born 150 9 orginal original 153 9 1307674368000 653837184000 8 158 17 remove “,” after cos(\theta) 159 3 lemma theorem 163 2 number number perfect 165 -16 can you you can 165 -13 point paint 9 169 -2 sgn sign 174 20 f \phi 176 -17 the cycle the same cycle 176 -10 (i_1,…,i_{n_2}) (i_{n_1+1},…,i_{n_2}) 176 -9 (i’_1,…,i’_{n_2}) (i’_{n_1+1},…,i’_{n_2}) 176 -10 (i_1,…,i_{n_k}) (i_{n_{k-1}+1},…,i_{n_k}) 176 -9 (i’_1,…,i’_{n_k}) (i’_{n_{k-1}+1},…,i’_{n_k}) 178 -13 ker(f)=\{e_2\} ker(f)=\{e_1\} 178 -15 g_1\cdot g_2^(-1)=e_2 g_1\cdot g_2^{-1}=e_1 180 -4 (i,j,k)(j,k,l) (j,k,l)(i,j,k) 180 -3 (i,j)(j,k) (j,k)(i,j) 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’ 223 -14 C_3^8 x S_V (2nd one) C_2^{12} x S_E 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 10^7 234 15 Therfore Therefore 238 17 c_{21}^1 and c_{21}^2 c_{22}^1 and c_{22}^2 241 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 12.4 282 11 Condider Consider 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”, instead of [Gar1]. 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 on page 115 was found by Doug McKenzie – 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!
Michael Chapman provided a long list of typos. His very careful reading is very much appreciated!
I think Haruyuki Kawabe for the remaining typos, as well as his Japanese translation of the book.