Errors and Misprints in "Handbook of Computational Group Theory"
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Tha authors are grateful to a number of people who have pointed out errors
in the text and particularly to Ken Brown, Cornell, for finding some of
the more subtle errors.
Mathematical errors
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Page 4, line 20. 196854 -> 196884 (it could also be 196883).
Page 26, line 7 of Section 2.3.1. Replace second $H \lhd K$ by $H \lhd G$.
Page 41, line -9. $tx \neq _F \overline{tx}^{-1} -> $tx \neq _F \overline{tx}$.
Page 41, line -3. $\hat{Y} \cap \hat{Y}^{-1}$ -> $\hat{Y} \cup \hat{Y}^{-1}$.
Page 71, line 21. $k$ -> $s$.
Page 75, line 2. $F$ -> $G$.
Page 75, lines -12 and -1. To solve (iv), if it was not assumed that
$K \le \im(\phi)$, then it would also be necessary to compute
the intersection of $K$ with $\im(\phi)$.
Page 79, line 6. Instead of "If $\beta^{x} \not\in \Delta$" it should be,
"If $\beta^{x}$ is not the first component of an element of $\Delta$".
Page 80, line 17. $v[4]$ -> $v[6]$; i.e. we put $v[6] = 2$.
Page 80, line -16. $X$ (same as for OrbitSv) missing from Input of U-Beta.
Page 84, line 11 of MinimalBlock. $q[l] := REP(\lambda)$ -> $q[l] := \lambda$.
Page 92, line -4. Finally, with $\beta = 4,$ -> Finally, with $\beta = 3,$
Page 103 Line 3 of BaseSwap procedure and lines 2 and -2 of text.
$\beta_{i+1}$ -> $\beta_i$.
Page 144, line 11. Note that the subscript $i$ in $g_i$ means `in-shuffle',
which is different from the other occurrences of $i$ on this line.
Page 144, lines -12 - -11. Structure of Sh(n) is wrong when n is a power of two.
Should be $C_2 \wr C_{r+1}$, where $n = 2^r$.
Page 151. The second line of the relator table at the top of the page
should be 2 2 1 1 2 (not 2 2 1 3 2).
Page 155, Procedure Scan, lines 9 and 10, and
Page 161, Theorem 5.5. Since we have not formally defined termination of the
algorithm, it could be unclear what this theorem says. The aim is in
fact to prove that Hypotheses (ii), (iii) and (iv) of Theorem 5.2 are
eventually satisfied.
Page 163, Procedure ScanAndFill, lines 10 and 11. $x_i^{-1}$ -> $x_j^{-1}$.
There should be a `return;' after line 13.
Page 156, statement of Proposition 5.3: $W$ -> $R$.
Page 179, line -10. $\tau(b)^u$ -> $\tau(b)^v$.
Page 180, line 12 of ModifiedCoincidence. $P[\mu,x^{-1}]$ -> $P[\nu,x^{-1}]$.
Page 198, line -9. valency -> order.
line -3. degree -> order.
Page 223, line 11. Replace $\mathcal{W}$ by $\mathcal{V}$.
Page 253, line -5. $u \in R^{rd}$ -> $u \in K^{rd}$.
Page 270, Case 6 of Theorem 7.3. $G/Z$ -> $G$.
Page 295, lines 2-4. The claim that $dep_X(u) > dep_X(g)$ is not correct.
To prove that the algorithm must terminate, note that Line 10 can only
be executes once for each value of $d$. It can also be shown that
$|\mathcal{G}| \le t + n + n^2$ at all times.
Page 381, line 20. abelian -> solvable.
Page 421, lines 9 and 17, and proof of Proposition 12.20.
It is not necessarily true that the simplification process does not
change the relation $\rightarrow^*$, and so the proof of
Proposition 2.20 dowes not work. We refer the reader to Section
2.6 (pages 76 - 83) of the book "Computation with Finitely Presented
Groups" by C.C.Sims for a correct treatment of the simplification
process.
Page 448, lines 12 and -12. Replace $v \in A^* \times A^*$ by $v \in A^*$.
Page 460, line -15 - -14. Or, more accurately:
Then, from the way that $W'$ was constructed, we know that there exists
$v \in A^*$ with $(w,v)^+ \in L(Z_\epsilon')$ and $v < w$".
Page 462, line -2. "If $L(E_x) = A^*$ ..." -> "If $L(E_x) = L(W')$ ..."
Other errors
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Page v, second paragraph should end with a full stop (period).
Page 63, line 11. The mathematical symbol 'G' is typeset as text.
Page 84, line 3. "Given" -> "given".
Page 157, line -18. have have -> have.
Page 162, line -7. Hazelgrove -> Haselgrove.
Page 227, line -17, Page 337, line -2, Page 347, line -4, Page 400, line 1. [Coh73] -> [Coh95].
Page 477, lines 13-15. 1973 -> 1995.
Page 272, line -6. Replace full stop (period) by comma.
Page 341, line 19, matrix $M$ be $ME$ -> matrix $M$ by $ME$.