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As the "second-generation" proof of the Classification of Finite Simple Groups is being written up in the volumes by Gorenstein, Lyons, Aschbacher, Smith, Solomon, and others (see e.g. this question) certainly much of the work will go into fixing minor (and possibly major) issues and gaps in the proof, since the first announcement in 1983.

Here are two such gaps:

  1. The classification of quasithin groups. G. Mason claimed a proof in an unpublished manuscript in 1981, but this was found to contain serious gaps. It would not be until 2004 that this gap would be fixed (see this behemoth, [1,2]).

  2. In 2008, Harada and Solomon [3] filled a minor gap in the classification by describing groups with a standard component that is a cover of the Mathieu group $M_{22}$, a case that was accidentally omitted from the proof of the classification due to an error in the calculation of the Schur multiplier of $M_{22}$ (from the Wikipedia page for CFSG).

I would like to see a longer such list! Thus:

What other (major or minor) gaps have been discovered, and subsequently fixed, in the proof of the CFSG, since the announcement in 1983?

Of course, if there are any gaps that are "known, but with a known fix" (but which have not yet made it into the aforementioned second-generation proof), then these would also be interesting to know.

${}$

References:

[1] Aschbacher, Michael; Smith, Stephen D., The classification of quasithin groups. I: Structure of strongly quasithin $\mathcal K$-groups., Mathematical Surveys and Monographs 111. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3410-X/hbk). xiv, 477 p. (2004). ZBL1065.20023.]

[2] Aschbacher, Michael; Smith, Stephen D., The classification of quasithin groups. II: Main theorems: the classification of simple QTKE-groups., Mathematical Surveys and Monographs 112. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3411-8/hbk). xii, pp. 479-1221. (2004). ZBL1065.20024.

[3] Harada, Koichiro; Solomon, Ronald, Finite groups having a standard component (L) of type $\widehat M_{12}$ or $\widehat M_{22}$., J. Algebra 319, No. 2, 621-628 (2008). ZBL1135.20009.

As the "second-generation" proof of the Classification of Finite Simple Groups is being written up in the volumes by Gorenstein, Lyons, Aschbacher, Smith, Solomon, and others (see e.g. this question) certainly much of the work will go into fixing minor (and possibly major) issues and gaps in the proof, since the first announcement in 1983.

Here are two such gaps:

  1. The classification of quasithin groups. G. Mason claimed a proof in an unpublished manuscript in 1981, but this was found to contain serious gaps. It would not be until 2004 that this gap would be fixed (see this behemoth).

  2. In 2008, Harada and Solomon filled a minor gap in the classification by describing groups with a standard component that is a cover of the Mathieu group $M_{22}$, a case that was accidentally omitted from the proof of the classification due to an error in the calculation of the Schur multiplier of $M_{22}$ (from the Wikipedia page for CFSG).

I would like to see a longer such list! Thus:

What other (major or minor) gaps have been discovered, and subsequently fixed, in the proof of the CFSG, since the announcement in 1983?

Of course, if there are any gaps that are "known, but with a known fix" (but which have not yet made it into the aforementioned second-generation proof), then these would also be interesting to know.

As the "second-generation" proof of the Classification of Finite Simple Groups is being written up in the volumes by Gorenstein, Lyons, Aschbacher, Smith, Solomon, and others (see e.g. this question) certainly much of the work will go into fixing minor (and possibly major) issues and gaps in the proof, since the first announcement in 1983.

Here are two such gaps:

  1. The classification of quasithin groups. G. Mason claimed a proof in an unpublished manuscript in 1981, but this was found to contain serious gaps. It would not be until 2004 that this gap would be fixed (see this behemoth, [1,2]).

  2. In 2008, Harada and Solomon [3] filled a minor gap in the classification by describing groups with a standard component that is a cover of the Mathieu group $M_{22}$, a case that was accidentally omitted from the proof of the classification due to an error in the calculation of the Schur multiplier of $M_{22}$ (from the Wikipedia page for CFSG).

I would like to see a longer such list! Thus:

What other (major or minor) gaps have been discovered, and subsequently fixed, in the proof of the CFSG, since the announcement in 1983?

Of course, if there are any gaps that are "known, but with a known fix" (but which have not yet made it into the aforementioned second-generation proof), then these would also be interesting to know.

${}$

References:

[1] Aschbacher, Michael; Smith, Stephen D., The classification of quasithin groups. I: Structure of strongly quasithin $\mathcal K$-groups., Mathematical Surveys and Monographs 111. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3410-X/hbk). xiv, 477 p. (2004). ZBL1065.20023.]

[2] Aschbacher, Michael; Smith, Stephen D., The classification of quasithin groups. II: Main theorems: the classification of simple QTKE-groups., Mathematical Surveys and Monographs 112. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3411-8/hbk). xii, pp. 479-1221. (2004). ZBL1065.20024.

[3] Harada, Koichiro; Solomon, Ronald, Finite groups having a standard component (L) of type $\widehat M_{12}$ or $\widehat M_{22}$., J. Algebra 319, No. 2, 621-628 (2008). ZBL1135.20009.

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As the "second-generation" proof of the Classification of Finite Simple Groups is being written up in the volumes by Gorenstein, Lyons, Aschbacher, Smith, Solomon, and others (see e.g. this question) certainly much of the work will go into fixing minor (and possibly major) issues and gaps in the proof.

One major gap in the proof of the CFSG that has been fixed, since the first announcement in 1983 concerned the classification of quasithin groups. G. Mason claimed a proof in an unpublished manuscript in 1981, but this was found to contain serious gaps. It would not be until 2004 that this gap would be fixed (see this behemoth).

For another gap, on the Wikipedia page for CFSG one finds thatHere are two such gaps:

"[in 2008], Harada and Solomon fill a minor gap in the classification by describing groups with a standard component that is a cover of the Mathieu group $M_{22}$, a case that was accidentally omitted from the proof of the classification due to an error in the calculation of the Schur multiplier of $M_{22}$."

  1. The classification of quasithin groups. G. Mason claimed a proof in an unpublished manuscript in 1981, but this was found to contain serious gaps. It would not be until 2004 that this gap would be fixed (see this behemoth).

  2. In 2008, Harada and Solomon filled a minor gap in the classification by describing groups with a standard component that is a cover of the Mathieu group $M_{22}$, a case that was accidentally omitted from the proof of the classification due to an error in the calculation of the Schur multiplier of $M_{22}$ (from the Wikipedia page for CFSG).

I would like to see a longer such list! Thus:

What other (major or minor) gaps have been discovered, and subsequently fixed, in the proof of the CFSG, since the announcement in 1983?

Of course, if there are any gaps that are "known, but with a known fix" (but which have not yet made it into the aforementioned second-generation proof), then these would also be interesting to know.

As the "second-generation" proof of the Classification of Finite Simple Groups is being written up in the volumes by Gorenstein, Lyons, Aschbacher, Smith, Solomon, and others (see e.g. this question) certainly much of the work will go into fixing minor (and possibly major) issues and gaps in the proof.

One major gap in the proof of the CFSG that has been fixed since the announcement in 1983 concerned the classification of quasithin groups. G. Mason claimed a proof in an unpublished manuscript in 1981, but this was found to contain serious gaps. It would not be until 2004 that this gap would be fixed (see this behemoth).

For another gap, on the Wikipedia page for CFSG one finds that

"[in 2008], Harada and Solomon fill a minor gap in the classification by describing groups with a standard component that is a cover of the Mathieu group $M_{22}$, a case that was accidentally omitted from the proof of the classification due to an error in the calculation of the Schur multiplier of $M_{22}$."

What other (major or minor) gaps have been discovered, and subsequently fixed, in the proof of the CFSG, since the announcement in 1983?

Of course, if there are any gaps that are "known, but with a known fix" (but which have not yet made it into the aforementioned second-generation proof), then these would also be interesting to know.

As the "second-generation" proof of the Classification of Finite Simple Groups is being written up in the volumes by Gorenstein, Lyons, Aschbacher, Smith, Solomon, and others (see e.g. this question) certainly much of the work will go into fixing minor (and possibly major) issues and gaps in the proof, since the first announcement in 1983.

Here are two such gaps:

  1. The classification of quasithin groups. G. Mason claimed a proof in an unpublished manuscript in 1981, but this was found to contain serious gaps. It would not be until 2004 that this gap would be fixed (see this behemoth).

  2. In 2008, Harada and Solomon filled a minor gap in the classification by describing groups with a standard component that is a cover of the Mathieu group $M_{22}$, a case that was accidentally omitted from the proof of the classification due to an error in the calculation of the Schur multiplier of $M_{22}$ (from the Wikipedia page for CFSG).

I would like to see a longer such list! Thus:

What other (major or minor) gaps have been discovered, and subsequently fixed, in the proof of the CFSG, since the announcement in 1983?

Of course, if there are any gaps that are "known, but with a known fix" (but which have not yet made it into the aforementioned second-generation proof), then these would also be interesting to know.

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