Groupprops:Error log/2011

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This is an archive of errors fixed in the year 2011. The criteria for logging an error are that either of these conditions hold:

• The error was on a highly trafficked page (more than 1000 cumulative pageviews so far) and stayed online for at least 24 hours.
• The error stayed online for at least a month.

Technical (computer-related) errors

• For some pages, due to editing from a mobile/NetFront browser, the entire page got truncated to the first 5 KB (roughly 5-6 scroll downs) and the rest of the page went missing. This happened to the quaternion group page: the truncation happened on July 1 and was fixed on July 3. It also happened to the linear representation theory of quaternion group page on July 2, but that was fixed within an hour.

Erroneous pages/statements

• August 21, 2011: A page titled normal not implies Lagrange-like incorrectly stated that a normal subloop in a finite loop need not be a Lagrange-like subloop, and gave a mistaken example (the example subloop wasn't normal). The correct statement is normal implies Lagrange-like.
• A page titled non-modular implies character-determining mistakenly stated that if the characteristic of a field does not divide the order of a finite group, then any linear representation over the field is determined by its character. In fact, the statement is true only in characteristic zero, for the silly reason that taking a representation with multiplicity $p$ gives a character that takes the value zero everywhere. The correct versions are at character determines representation in characteristic zero and character does not determine representation in any prime characteristic

Factual errors in high traffic pages

These errors are in pages that had received over 1000 cumulative pageviews at the time the error was fixed.

Page	Error description	Version where it was introduced	Version where it was corrected	Why error? Why not caught? ("I" refers to Vipul)
classification of finite abelian groups	Had $m_1$ in place of $p^{m_1}$ at one place, similar errors on that line		December 31, 2011	hadn't visited page often
quaternion group	Two wrong "Verbal definitions" involving holomorphs, which should have been with dihedral group:D8	May 13, 2007 (page creation)	June 29, 2011	The error slipped my notice because I didn't ever actually read these other Verbal definitions. Beware of additional definitions.
quaternion group	Typographical errors in verbal description relating $i,j,k$ (-1 instead of -i at one place, missing comma at another). The error was not there in the multiplication table, which was more prominent.	May 13, 2007 (page creation)	June 29, 2011	Detail, something I skip when reading
dihedral group:D8	Wrong additional definition involving another alternative presentation	March 26, 2010	June 29, 2011	It somehow didn't register, because I knew a definition "like" this is correct (which it is)
dihedral group:D8	Had one double transposition repeated, instead of writing another one that I should have, in the "definition as a permutation group" section	March 26, 2010	June 21, 2011	minor detail, didn't notice
dihedral group:D8	Had an error in the count for number of conjugacy classes of subgroups, had written "7" instead of "8"			didn't know the count offhand, so error didn't jar when reading
dihedral group:D8	In the "Description by presentation" section under GAP implementation, the F := FreeGroup(2); line was missing but instead the next line occurred twice.			minor detail, didn't notice.
linear representation theory of quaternion group	Had number of irreducible representation as "3" instead of "5" even though there were 5 of them listed above	April 20, 2011	July 1, 2011	The error probably originated because I copied from linear representation theory of symmetric group:S3 and failed to modify. It lasted because I didn't pay much attention to that line since the line above -- the actual list of degrees -- was correct.
linear representation theory of dihedral group:D8	wrote "any field of characteristic not two or three" instead of "any field of characteristic not two" in the summary	April 20, 2011	May 22, 2011	minor detail, didn't notice.
linear representation theory of dihedral group:D8	"Smallest ring of realization" item, column on matrix entry list, had missing representations and wrong information on one representation	April 5, 2010	June 29, 2011	far down in page
linear representation theory of dihedral group:D8	In the description of the two-dimensional irreducible representation, interchanged row entries for "characteristic polynomial" and "minimal polynomial"	June 29, 2011	July 1, 2011	simply didn't notice, two columns already quite similar. Caught in two days.
linear representation theory of quaternion group	Mistakenly wrote that if -1 is not a square, the field is not a splitting field.		July 2, 2011	genuine conceptual misunderstanding
symmetric group:S3	In the list of orders of subgroups, omitted the order of the whole group.	September 4, 2009	July 3, 2011	Not a very consequential or confusing error, because there was both a link to more detail elsewhere, and more detailed and correct information right below it. Got ignored while reading.
quaternion group	Mistakenly wrote "Yes" for whether it's a rational-representation group, although the internal semantic storage was that it isn't, and the explanation on the side hinted that it isn't. (The explanation said "two-dimensional representation that is not rational" and the comment on the side said "Contrast with dihedral group:D8, that is a rational-representation group"	May 13, 2009	July 3, 2011	Far down in page, skipped notice.
alternating group:A5	Had a "10" instead of a "5" in an explanation for function value (not in the actual function value, which was correct at "5"). Very minor, clear error, not confusing.		July 6, 2011	Error buried in explanation, analogous to typo.
linear representation theory of symmetric group:S4	In the hook length formulas for the standard representation and product of standard and sign representations, had $4 \cdot 2 \cdot 2 \cdot 1$ in the denominator instead of $4 \cdot 2 \cdot 1 \cdot 1$.		July 11, 2011	Minor detail, didn't check formula
linear representation theory of symmetric group:S4	Error in two of the cell entries for the size-degree-weighted character table (the original character table was correct)		July 16, 2011	Minor detail, didn't check
symmetric group:S5	Wrote $S_4$ in place of $S_5$ in the Automorphisms section		October 1, 2011	copy-and-paste error.

Factual errors in low traffic pages

Page	Error description	Version where it was introduced	Version where it was corrected	Why error? Why not caught? ("I" refers to Vipul)
Sanov subgroup in SL(2,Z)	Had "1" instead of "2" in some matrix entries	March 30, 2011	November 24, 2011 (by David Loeffler)	typo, didn't visit page often (the definition in the page Sanov subgroup in SL(2,Z) is free of rank two was correct)
special linear group of degree two	error in general expression for multiplication of $2 \times 2$ matrices		November 7, 2011	didn't check the expression.
replacing a subgroup by a normal subgroup			November 7, 2011
projective general linear group	Stated inaccurate condition for $PGL(n,q) = PSL(n,q) = SL(n,q)$; the original formulation is correct only for $n = 2$		November 7, 2011
second cohomology group for trivial group action	Confusing lead lines, confused wording with definition of second cohomology group		September 30, 2011
commensurator of subgroup is subgroup	Wrote $g^{-1}Hg$ at one place instead of $g^{-1}Hg \cap H$	February 19, 2011	September 16, 2011
constrained for a prime divisor implies not simple non-abelian	wrong definition of p-constraint in use	March 2, 2009	September 16, 2011	did not revisit page after conceptual confusion was cleared, page in obscure location
Second cohomology group for trivial group action of V4 on Z2	linked to direct product of D8 and Z4 instead of central product of D8 and Z4 at one place		September 14, 2011	minor error, far down in page
SmallGroup(128,1015)	forgot to equate a chain equality to the identity element in a presentation	July 18, 2011	September 14, 2011	minor error, hadn't visited page often
Finite group having at least two conjugacy classes of involutions has order less than the cube of the maximum of orders of centralizers of involutions	Wrote $m$ in place of $h$ in the Given section of the proof.		September 12, 2011	minor error
Corollary of centralizer product theorem for rank at least three	Forgot the rank at least three in the Given part of the proof section (it was included in the main text of the statement).		September 12, 2011
Pi-separable and pi'-core-free implies pi-core is self-centralizing	Had "=" instead of $\le$ in the main statement		September 11, 2011
p-solvable implies p-constrained	wrote $P$ in place of $Q$ at one place.		September 11, 2011
D8 versus Q8	wrong name of group in one of the captions to the lattice diagrams.		September 7, 2011
A4 in S4	Slightly wrong reason for why it is the subgroup generated by squares	?	August 23, 2011	minor error, didn't notice
Congruence condition on number of subgroups of given prime power order	Mistaken normal subgroup version		August 18, 2011, further fix September 2, 2011	Slight conceptual confusion, juggling editing multiple versions of statement.
Fusion systems for dihedral group:D8	a few minor errors in description, the whole thing was rewritten		August 4, 2011
Mathieu group:M9	Fitting length was mis-stated as 1, it should be 2		July 31, 2011	minor error, went unnoticed. Possibly typo.
Groups of order 168	Typographical error, 169 instead of 168	May 23, 2011	July 30, 2011	Minor typographical error
Mathieu group:M11	Mistakenly wrote that $M_{21}$ is not a simple group. The correct version is that it is simple but not a sporadic simple group.	September 2, 2009	July 30, 2011	confusion at the time of writing the page.
element structure of general linear group of degree two over a finite field	Error with description of centralizers of elements of Jordan blocks of size two -- mistakenly assumed it is GA(1,q) and also called it a Borel subgroup		July 20, 2011
element structure of special linear group of degree two over a finite field	minor errors -- fixed semisimple or unipotent to semisimple or unipotent or negative times unipotent and also some place with a $q - 1$ instead of a $q$		July 20, 2011
element structure of special linear group:SL(2,3)	Had one of the conjugacy class representative matrices wrong/repeated	October 13, 2010	July 17, 2011	Minor error, page not frequently visited.
element structure of symmetric group:S6	mistakenly clubbed two conjugacy classes of size 90 into a single automorphism class		July 16, 2011
element structure of groups of order 64	had one of the totals of rows entries in a row cell as "24" instead of "22" -- easy to catch upon inspection	June 12, 2011	July 15, 2011	minor error, escaped notice. Finally caught based on congruence mod 3 condition.
grand orthogonality theorem	Mistakenly stated the inner product with itself as $n/|G|$ instead of $1/n$.		July 13, 2011	Page was low priority, hadn't read it for long
column orthogonality theorem	Slight mistake in formulation for non-splitting fields, ignored the case of positive Schur index			Subtle error, page low priority
order of periodic element of general linear group over integers is bounded	had mistakenly stated bound in terms of Euler totient function, proof wrong (though the erroneous part of proof was marked Fill this in later)	October 6, 2008	July 11, 2011	genuine confusion, had been told the wrong result
free group:F2	Stated wrongly that it is not Hopfian in the "Group properties" section	September 10, 2009	July 3, 2011	Might have had a misconception when creating the page, or been careless. Hadn't visited the page frequently, also, obscure location within page.
linear representation theory of special linear group:SL(2,3)	Had "maximum degree of irreducible representation" as 2 instead of 3, even though listing above was correct	April 20, 2011	July 1, 2011	Either a typo or a copy-paste error. Hadn't visited the page much, so probably lasted because I didn't have enough opportunities to catch the error.
semidihedral group:SD16	Mistakenly stated under "Group properties" that this is a group in which every normal subgroup is isomorph-free. What I meant to say is that every normal subgroup is normal-isomorph-free?	September 13, 2009	July 4, 2011	Slight confusion at the time of page creation; also, hadn't read the page frequently.
A4 in S4	Had a semantic labeling error, not visible in actual text, on whether the subgroup is homomorph-containing (the actual text read fine)	December 1, 2010	July 8, 2011	error in semantic labeling, not visible in page.
homomorph-containing subgroup	One of the rows in the Stronger Properties table was messed up (in appearance and minor content error too)	November 12, 2009	July 8, 2011