Groupprops:Error log

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Did you find something that looks like an error (or possible error) to you? Report the error quickly here (anonymous, does not require login, but you can optionally provide an email ID to be notified of the fix).

See below for some errors that have been caught and fixed in the past.

As we try to make Groupprops more reliable, this log is intended to keep a record of errors that satisfy either of these two criteria:

  • 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.

The log was started in 2011. This page lists the errors fixed in 2012 and later. The log of errors fixed in 2011 is at Groupprops:Error log/2011.

Note that the page does not list spelling and formatting errors if those errors do not affect the mathematical or factual meaning of the content. The page does list major formatting errors on high traffic pages that create trouble with displaying or understanding part of the text.

Factual errors in high traffic pages

These include glaring factual errors of commission or omission.

Page Error description Version where it was introduced Version where it was corrected Why error? Why not caught? ("I" refers to Vipul)
Groups of order 18 direct product of S3 and Z3 was marked as not metacyclic, though it is September 17, 2009 February 18, 2017 carelessness
2-Sylow subgroup of special linear group:SL(2,5) The subgroup was wrong. Four of the elements were not even in SL(2,5). June 28, 2011 October 26, 2016 carelessness, this edit was made a long time ago before proper procedures were in place for error detection
Nilpotent group Had a duplicate row on torsion-free nilpotent group, with one of the duplicates giving incorrect information September 9, 2016 carelessness or misconceptions at the time of addition of the incorrect row
Element structure of special linear group:SL(2,5) One place in a table had a factor of 2 in one description that shouldn't have been there August 13, 2016 carelessness
Finite and any two maximal subgroups intersect trivially implies not simple non-abelian The description of Step (2) referenced Step (3) whereas it should have been Step (1 ) June 20, 2016 Error only in expandable box that's collapsed by default, and not in proof logic itself.
Zassenhaus isomorphism theorem Incorrect statement of one of the terms in the theorem, wrote instead of May 30, 2016 careless, also did not revisit the page to review
subgroup structure of groups of order 24 Incorrectly stated number of 2-subgroups for groups of IDs (24, 6) and (24, 7) February 22, 2016 line copy off-by-one error
index is multiplicative roles of subgroups were interchanged in part of the proof November 15, 2015 change in notation midway through article creation process
element structure of symmetric group:S3 and (by inclusion) symmetric group:S3 in table, indicated that the 3-cycle conjugacy class does not split in the alternating group in S3. August 29, 2015 carelessness, insufficient review of table contents
automorphism group of alternating group:A6 wrote that the automorphism group of the alternating group of degree three is the symmetric group, but actually it's the cyclic group of order two. June 7, 2015 carelessness, forgot that being abelian introduces complications.
Coxeter group for symmetric group and direct product, stated that some entries are 0 when they're actually 2; also a typo in one of the matrices with an entry marked as 3 when it should be 2. May 15, 2015 insufficient attention to detail in a complex page on a topic I didn't have a lot of prior knowledge of.
simple non-abelian group Forgot to say "normal" when invoking the definition of simple group May 15, 2015 carelessness, insufficient page review
normal subgroup The summary description of the second isomorphism theorem in the Isomorphism theorems section stated the condition as " is contained in the normalizer of " rather than " is contained in the normalizer of ." November 10, 2014 carelessness, insufficient proofreading
groups of order 81 somewhere on the page, incorrectly listed the groups with IDs 9 and 10 as having nilpotency class 2 instead of 3, though the correct value had been listed above June 8, 2014 (here and here) Carelessness, reasons for slip unclear
automorphism group of a group wrote the automorphism group of cyclic group:Z8 as cyclic group:Z4 instead of Klein four-group February 25, 2014 didn't review the page carefully
element structure of projective general linear group of degree two over a finite field One of the multiplied-out formulas for the total number of elements was wrong, though the factored form was correct (missed a factor of in the multiplication) February 3, 2014 Only cross-checked the answer in factored form.
subgroup structure of alternating group:A6 (error also propagated via inclusion in alternating group:A6 wrote one of the generators as rather than as . December 31, 2013 careless analogy with twisted S3 in A5
element structure of alternating group:A4 In the section element structure of alternating group:A4#Multiple ways of describing permutations, had listed as a permutation in the group. November 18, 2013 carelessness, didn't check long list.
a template error on the template page Template:Subgroups dissatisfying property sorted by importance rank resulted in some incorrect examples being displayed for central factor (although the incorrect template was also used on the normal subgroup page, no incorrect examples were displayed there as a result). January 19, 2013 February 16, 2013 the error was in a very limited subset of the examples generated, and not in the most prominent examples, so it escaped notice.
alternating group incorrect description of exponent for the case of odd August 27, 2009 February 1, 2013 carelessness; the right formula was used on other pages such as the page on alternating group:A5.
special linear group:SL(2,3) mistakenly stated that every automorphism of GL(2,3) is inner January 20, 2013
central factor In one of the equivalent formulations of the definition, forgot to state the precondition of normality necessary for the rest of the definition to make sense January 19, 2013
characteristicity is transitive In the "Given" of the "Hands-on proof" wrote that is characteristic in instead of being characteristic in October 20, 2008 June 27, 2012 didn't check carefully
linear representation theory of symmetric group:S3 didn't state the size of the conjugacy class of the 2-transposition in the character table column header July 16, 2011 June 3, 2012 copy-paste error when shuffling columns
symmetric group:S3 In one of the explanations, stated that the group is an ambivalent group, but the observation that needed to be made was that the group is a rational group. June 29, 2011 May 31, 2012
group for the "minimum number of variables needed to describe condition" column, I had "2" instead of "1" for inverse element. February 25, 2011 May 5, 2012 didn't review/revist page often enough
symmetric group:S7 error in the code link for "similar groups" April 28, 2012 error not directly visible on page, only upon clicking link
groups of order 16 had instead of as the Hall-Senior symbol for elementary abelian group:E16 April 17, 2012 minor error on long page
alternating group:A6 forgot factor of half in order formula for PSL(2,q) March 19, 2012
special linear group:SL(2,3) forgot to include whole group in list of normal subgroups February 29, 2012, also changing the format of the page minor
symmetric group:S4 used formula instead of for number of conjugacy classes in February 22, 2012 genuine misconception, got cleared when creating the page for element structure of general affine group of degree two over a finite field
linear representation theory of symmetric group:S4 mistakenly stated in the section on orthogonality relations and numerical checks that there are no abelian normal subgroups February 20, 2012 far down in page

Other errors in high traffic pages

These include formatting and display errors, as well as minor errors of omission.

Page Error description Version where it was introduced Version where it was corrected Why error? Why not caught? ("I" refers to Vipul)
subgroup structure of symmetric group:S3 Two minor issues in the Conjugacy class-defining functions section: a dangling math tag in the first row, and a missing cell in the second row causing a column alignment problem September 23, 2016 (edit 1, edit 2) carelessness, insufficient review
normal subgroup generated by a subset Used instead of in describing the containment of the subset in a subgroup May 8, 2014 carelessness
cyclic group:Z2 wrong link, some poor grammar in an explanation for the number of conjugacy classes. January 20, 2013
element structure of alternating group:A4 messed up some column alignments series of edits culminating in this. Most of the errors were fixed within the 24-hour grace period for error reporting. didn't check column alignments
element structure of symmetric group:S3 used "formula for number of conjugacy classes" in a column header instead of "formula for order" although the section header and other language made it clear this refers to a formula for the order. November 24, 2012
finite solvable group couple of rows with column mis-alignments June 5, 2012
dihedral group:D8 the subgroup lattice diagram overlapped partially with the subgroup structure table The error was likely propagated by a font size change made to an automatically included text from the subgroup structure of dihedral group:D8 page with this edit on January 8, 2012. May 31, 2012. Also reverted the size edit on the other page didn't realize how size changes could impact pages where the text is included, so didn't check for that.

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)
Finite non-nilpotent and every proper subgroup is nilpotent implies not simple Reasoning had a slight error; a statement made universally was established only existentially, and needed to be modified to intermediate strength to make the logic work. December 20, 2011 June 19, 2016 subtlety, didn't catch
2-generated group said "comprises two elements" instead of "comprises at most two elements" for the generating set December 23, 2014 not thinking of edge cases
Automorph-conjugacy is not finite-intersection-closed Used curly braces (set notation) instead of angled braces (subgroup generated notation) when describing the subgroup December 19, 2014
Powering-invariant over quotient-powering-invariant implies powering-invariant Statement was incomplete, didn't include the conclusion to be proven from the hypothesis. December 19, 2014
Powering-invariance is not quotient-transitive The explanation of the third bullet point in the proof ( is not powering-invariant in ) was incorrect. December 19, 2014
Split algebraic group original definition made it appear as if the Borel subgroup is unique and/or that the condition being true on one Borel subgroup is equivalent to it being true on any other. May 5, 2014 genuine confusion, not enough effort to clarify the definition.
Recursively presented group stated the generating set must be finite, the more standard definition allows for countably infinite generating set May 31, 2007 November 5, 2013 genuine confusion as to what definition is more standard
Supersolvable implies nilpotent derived subgroup Had rather than October 16, 2013
Compatible pair of actions used action-on-each-other symbols instead of conjugation action symbols for one of the alternate definitions September 13, 2013 carelessness
Linear representation theory of general linear group:GL(2,3) incorrectly stated that the binary octahedral group has the same character table (the groups are isoclinic, so they have the same character degrees, but not the same character table) September 2, 2013 either carelessness or conceptual confusion at the time of page creation
Linear representation theory of general linear group:GL(2,3) a -1 and 1 were swapped in the description of the last character August 31, 2013 checked only a sample of entries, not all
Deducing the Baker-Campbell-Hausdorff formula from associative algebra manipulation off by constants, forgot to subtract 1 from a non-critical alternative description August 18, 2013
Baer Lie group stated "torsion-free" instead of "2-torsion-free" though the link was correct August 5, 2013 minor carelessness.
algebraic group is topological group under Zariski topology (deleted page) wrong page (entirely) July 27, 2013 although the conceptual error was fixed a while back, this particular page didn't get deleted.
linear representation theory of groups of order 96 For groups of GAP-ID 224 and 225 (3rd column of the table), the 3 irreducible representations are of degree 4, not of degree 6. July 9, 2013 carelessness, not enough review of table entries
groups of order 5 wrote "2 is a prime number" instead of "5 is a prime number" April 19, 2011 May 3, 2013
groups of order 3 wrote "2 is a prime number" instead of "3 is a prime number" April 19, 2011 May 3, 2013
Galois extensions for dihedral group:D8 said "neither nor " instead of "neither nor " May 2, 2013
RSA algorithm wrote "congruent to the order of the group" instead of "congruent to 1 modulo the order of the group" May 2, 2013
group cohomology of dihedral group:D8 wrote instead of January 15, 2013 April 2, 2013 The error was due to copy/paste from group cohomology of dihedral group:D16 without appropriate modification.
Schur-trivial group small issues of wrong words used in verbal explanations for reverse impliation falures. February 24, 2013
Characteristic not implies amalgam-characteristic had instead of at one intermediate step of explanation. February 21, 2013
No nontrivial homomorphism to quotient group not implies complemented stated example using GL(2,3) instead of the binary octahedral group. February 16, 2013, with a redirect to No nontrivial homomorphism to quotient group not implies complemented normal carelessness and/or confusion.
Classification of finite 2-groups of maximal class Didn't clarify the exception for where the semidihedral group doesn't exist February 8, 2013 carelessness
Field generated by character values stated that it is a cyclotomic extension of the rationals; the correct version is that it is contained in a cyclotomic extension of the rationals. July 13, 2011 January 31, 2013 careless error
Tour:Factsheet one (beginners) omitted the adjective "associative" in one of the definitions. July 26, 2008 January 31, 2013
Dicyclic group:Dic20 had missing relation in alternate presentation September 17, 2009 January 15, 2013 carelessness, low priority page
Ascendant subgroup and Descendant subgroup did not specify behavior at limit ordinals, making the definition vacuously true for all subgroups in all groups March 23, 2007 (for ascendant subgroup) and March 23, 2007 (for descendant subgroup) December 20, 2012 (for ascendant subgroup) and December 20, 2012 (for descendant subgroup) careless, didn't visit page often
Groups of order 720 listed one of the groups as Mathieu group:M11 instead of Mathieu group:M10 December 18, 2012 carelessness
Frattini quotient made statement for finite nilpotent group that is only valid for a finite p-group, namely that the Frattini quotient is elementary abelian November 25, 2012 careless error
Group cohomology of Klein four-group In section "cohomology groups for trivial group action" subsection "over an abelian group" the table entry for read instead of November 22, 2012 typo
Semidihedral group had a "+1" instead of "-1" in the presentation definition July 19, 2010 October 24, 2012 typo, didn't read carefully
Topological group incorrectly stated that algebraic groups are topological groups July 30, 2012
Characteristic not implies fully invariant in finite abelian group wrote in place of at one place July 3, 2012 copy-paste from earlier example, didn't fix
Derivation-invariance is transitive did not state " is a derivation-invarant subring of " as part of the Given in the proof section October 8, 2008 (first revision) June 27, 2012 didn't check carefully
Skew of 2-cocycle for trivial group action of abelian group is alternating bihomomorphism used left instead of right at one place June 24, 2012
Tour:Inquiry problems one (beginners) forgot to state what times is, and did not clearly state that the multiplication rules are for multiplication both ways June 23, 2012 and more edit, last one June 25, 2012
semitopological group had definition of quasitopological group instead, thought they mean the same thing June 23, 2012, corrections across multiple pages
left-topological group had interchanged roles of left and right in definition June 23, 2012
Right-associative elements of magma form submagma Had written "left" instead of "right" in a few places in the proof of part (3) involving nil elements June 20, 2012 (two edits) didn't revisit page
verifying the group axioms not really an error, but rather, an omission. Didn't check that the so-called inverse map is actually well defined from to . June 19, 2012 (final of a series of minor edits)
linear representation theory of special linear group of degree two over a finite field wrote maximum degree of irreducible representation is , but this is not true for June 17, 2012 didn't check exceptional small cases
Classification of groups of order four times a prime congruent to 3 modulo 4 wrote 4 divides instead of 4 divides , did not state June 14, 2012 did not revisit page
formal group law stated that all of acquires a group structure, instead of the maximal ideal June 13, 2012
normal subgroup of finite group in (3) of the three equivalent definitions, didn't state the clause that the whole group is finite June 6, 2012
black-box group algorithm for finding the subgroup generated by a subset used in place of at one place June 1, 2012 Change of notation, didn't completely verify that the change was propagated everywhere
linear representation theory of groups of order 16 a couple of sentences in the "grouping by Hall-Senior families" section referred to order 32 instead of 16, though the mathematical content wasn't affected May 31, 2012
general affine group and related pages mistakenly assumed that all extensions over prime subfield are Galois, used instead of May 31, 2012 (multiple edits on multiple pages)
element structure of special linear group of degree two over a finite field wrote "characteristic 3" in place of "odd characteristic" at one place. While the statement was correct, it did not constitute the explanation it purported to be May 31, 2012
Kunneth formula for group homology Had in place of at one place May 29, 2012 notation change, didn't fix all symbols
symmetric subset In the definition, said the following equivalent conditions instead of both the following conditions June 13, 2007 May 26, 2012 didn't visit page often enough
Hall not implies order-isomorphic wrote down order of in place of at one place and mis-stated one of the Hall subgroups May 21, 2012
Burnside group interchanged roles of parameters to describing the Burnside group May 20, 2012
first cohomology group superscripts instead of at some places. May 10, 2012 copy-paste error.
faithful irreducible representation of quaternion group mistakenly used the word "representation" instead of "character" in the summary table April 29, 2012 minor error, didn't review/revisit page enough
faithful irreducible representation of dihedral group:D8 did not say "of characteristic not two" at one of two places in the "Embeddings" section April 29, 2012 minor error, didn't review/revisit page enough
symmetric group:S8 error in link code for "similar groups" April 28, 2012 error not visible on page, need to click link or observe carefully
fusion systems for dihedral group:D8 excluded one of the possibilities for the fusion system April 26, 2012 conceptual confusion, didn't think about this enough
element structure of special linear group of degree two over a finite discrete valuation ring In the formula for the order of the group, the exponent on read and it should read November 4, 2011 March 30, 2012 confused, didn't devote adequate thought to the computation, didn't revisit often enough
Weyl group one of the equivalent definitions used the word "kernel" instead of the word "image" March 30, 2012 didn't visit page frequently
imperfect group Stated mistakenly that hypoabelian implies imperfect. September 9, 2009 March 22, 2012 confusion about transfinite behavior
Minimal splitting field need not be cyclotomic mistakenly stated that every minimal splitting field is contained in a cyclotomic extension of the rationals. The correct version is that every finite group has a minimal splitting field that is contained in a cyclotomic extension of the rationals. February 29, 2012 The error was introduced at a time when I was unclear about this topic, and I didn't correct it even after it became clearer.
Number of irreducible representations over rationals equals number of equivalence classes under rational conjugacy Used word "reals" instead of "rationals" at one place February 19, 2012 Minor typo
Number of irreducible representations over rationals equals number of equivalence classes under rational conjugacy Had the false sentence "Note that the statement is not true for an arbitrary finite group. February 19, 2012 The error arose from an earlier version of the page/statement. It didn't get fixed when transitioning to the new version.
element structure of special linear group:SL(2,5) wrong description of eigenvalue pairs for one of the conjugacy classes February 18, 2012 minor detail
element structure of special linear group:SL(2,5) had "3" instead of "2" in one of the coefficients of a characteristic polynomial February 18, 2012
element structure of special linear group of degree two over a finite field Mistakenly stated the minimal polynomial as when it should have been two fixes, first one messed up, second one right: February 18, 2012 didn't proofread
element structure of special linear group of degree two over a finite field Mistakenly stated the minimal polynomial as when it should have been February 18, 2012 didn't proofread
element structure of general linear group of degree two over a finite field Mistakenly stated the minimal polynomial as when it should have been February 18, 2012 didn't proofread
non-associative ring listed associativity as one of the compatibility conditions March 3, 2010 February 17, 2012 carelessness, not visited page often
linear representation theory of semidihedral group:SD16 wrong column headers for two columns in the character table February 5, 2012
upper central series may be tight with respect to nilpotency class had a wrong example, too strong a statement February 2 (first edit), February 2 (second edit) carelessness
linear representation theory of M16 had and in place of at some places January 16, 2012
groups of order 32 wrote "7" instead of "5" in explanation for why there are 7 abelian groups of order 32 January 16, 2012
linear representation theory of groups of order 32 in the section on classification up to isoclinism, the derived subgroup for was stated as cyclic group:Z2 when it is in fact cyclic group:Z4. January 16, 2012 copied from groups of order 32 page that had a similar error.
groups of order 32 in the section on classification up to isoclinism, the derived subgroup for was stated as cyclic group:Z2 when it is in fact cyclic group:Z4. January 16, 2012 details
extended centralizer mistaken statement about relation between being a real element and extended centralizer equal to centralizer July 25, 2009 January 15, 2012 did not visit page
group of Glauberman type for a prime missed out on quantifying as a -Sylow subgroup of January 14, 2012
equivalence of definitions of group of Glauberman type for a prime missed out on quantifying as a -Sylow subgroup of January 14, 2012
p-normal group said "contains " instead of "contains " at a couple of places January 14, 2012 didn't visit page
Connected topological group Mistakenly stated that connected iff no proper open subgroup January 12,2012 The statement is true in some contexts, e.g., for locally connected groups.

Other errors in high traffic pages

These include formatting and display errors, as well as minor errors of omission.

Page Error description Version where it was introduced Version where it was corrected Why error? Why not caught? ("I" refers to Vipul)
Finite non-nilpotent and every proper subgroup is nilpotent implies not simple Some key terms in the statement were missing, make it incomprehensible (specifically, because of the use of [[fact about::nilpotent group;3| ]]) December 20, 2011 June 20, 2016 error introduced after version upgrades/formatting changes later