update on vol 10 to appear later this year; page lengths
Source Link
David Roberts
  • 33.2k
  • 10
  • 113
  • 316

So it seems Stroth will contribute one volume, to go at the end, and we will have volume 11 (and maybe vol 12) of the main series before that. So 11+2+1 (or 12+2+1) volumes in total. [edit: the +2 is the Aschbacher–Smith work, the +1 is Stroth]

EDIT 9 October 2023

Commenter colt_browning points out below that Volume 10 is due for publication 26th December, and is now available for preorder: https://bookstore.ams.org/surv-40-10. The title is The Classification of the Finite Simple Groups, Number 10: Part V, Chapters 9–17: Theorem $C_6$ and Theorem $C^*_4$, Case A, with listed authors Capdeboscq, Gorenstein, Lyons and Solomon, and it's 570 pages long.

This book is the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see Mathematical Surveys and Monographs, Volume 40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.

Total length of volumes 1–10 is 4511 pages, and Aschbacher and Smith's two volumes fill 1320 pages. Maybe another 1000–1500 pages to go? There's an old manuscript of Stroth from the late 90s that seems to cover the "uniqueness case" (first listed article on this page), which is what his volume will cover. That's 244 pages, but it's not clear how it relates to the draft of what will become the last volume of the published second generation proof.

So it seems Stroth will contribute one volume, to go at the end, and we will have volume 11 (and maybe vol 12) of the main series before that. So 11+2+1 (or 12+2+1) volumes in total.

So it seems Stroth will contribute one volume, to go at the end, and we will have volume 11 (and maybe vol 12) of the main series before that. So 11+2+1 (or 12+2+1) volumes in total. [edit: the +2 is the Aschbacher–Smith work, the +1 is Stroth]

EDIT 9 October 2023

Commenter colt_browning points out below that Volume 10 is due for publication 26th December, and is now available for preorder: https://bookstore.ams.org/surv-40-10. The title is The Classification of the Finite Simple Groups, Number 10: Part V, Chapters 9–17: Theorem $C_6$ and Theorem $C^*_4$, Case A, with listed authors Capdeboscq, Gorenstein, Lyons and Solomon, and it's 570 pages long.

This book is the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see Mathematical Surveys and Monographs, Volume 40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.

Total length of volumes 1–10 is 4511 pages, and Aschbacher and Smith's two volumes fill 1320 pages. Maybe another 1000–1500 pages to go? There's an old manuscript of Stroth from the late 90s that seems to cover the "uniqueness case" (first listed article on this page), which is what his volume will cover. That's 244 pages, but it's not clear how it relates to the draft of what will become the last volume of the published second generation proof.

update with info from Lyons
Source Link
David Roberts
  • 33.2k
  • 10
  • 113
  • 316

EDIT 24 June 2023

I emailed Richard Lyons to double check how things are going given the hopeful progress on volume 10, mentioned above. He replied (and he and Ron Solomon gave permission to relay this):

Volume 10 has been submitted for publication.

I have received Stroth's final manuscript for the Uniqueness Case, which we plan to make the final volume.

[Ron] Solomon and I are currently working on Volume 11, the penultimate volume (provided that it fits into one volume .. it is not clear at this time whether it will or not). This will complete the proof of Theorem C_4 (the last of the seven in the Classification Grid) and begin the treatment of the Uniqueness Case for groups of even type, to mesh with Stroth's work.

So it seems Stroth will contribute one volume, to go at the end, and we will have volume 11 (and maybe vol 12) of the main series before that. So 11+2+1 (or 12+2+1) volumes in total.

EDIT 24 June 2023

I emailed Richard Lyons to double check how things are going given the hopeful progress on volume 10, mentioned above. He replied (and he and Ron Solomon gave permission to relay this):

Volume 10 has been submitted for publication.

I have received Stroth's final manuscript for the Uniqueness Case, which we plan to make the final volume.

[Ron] Solomon and I are currently working on Volume 11, the penultimate volume (provided that it fits into one volume .. it is not clear at this time whether it will or not). This will complete the proof of Theorem C_4 (the last of the seven in the Classification Grid) and begin the treatment of the Uniqueness Case for groups of even type, to mesh with Stroth's work.

So it seems Stroth will contribute one volume, to go at the end, and we will have volume 11 (and maybe vol 12) of the main series before that. So 11+2+1 (or 12+2+1) volumes in total.

recent news
Source Link
David Roberts
  • 33.2k
  • 10
  • 113
  • 316

EDIT 09 Mar 2023

From a 23 January 2023 article about Inna Capdeboscq (emphasis added):

The expected length of the Generation-2 proof is of about 5,000 pages published in 12 volumes. At this moment Volumes 1 through 9 are published. Inna has been involved in the Generation-2 project for several years, providing small contributions to Volume 6 and 7. Inna co-authored the recently published Volume 9 and is currently in a process of completing Volume 10.

I don't know how this estimate of 12 volumes sits with Solomon's email from January 2021 (see the Sept '21 edit) saying there would be 4 more volumes after vol 9 was done. And though Stroth's future contribution is mentioned in the short article, I don't think this count of 12 includes his manuscript mentioned above.

EDIT 09 Mar 2023

From a 23 January 2023 article about Inna Capdeboscq (emphasis added):

The expected length of the Generation-2 proof is of about 5,000 pages published in 12 volumes. At this moment Volumes 1 through 9 are published. Inna has been involved in the Generation-2 project for several years, providing small contributions to Volume 6 and 7. Inna co-authored the recently published Volume 9 and is currently in a process of completing Volume 10.

I don't know how this estimate of 12 volumes sits with Solomon's email from January 2021 (see the Sept '21 edit) saying there would be 4 more volumes after vol 9 was done. And though Stroth's future contribution is mentioned in the short article, I don't think this count of 12 includes his manuscript mentioned above.

edited body
Source Link
Denis Serre
  • 50.6k
  • 10
  • 143
  • 290
Loading
added 168 characters in body
Source Link
David Roberts
  • 33.2k
  • 10
  • 113
  • 316
Loading
Bounty Ended with 50 reputation awarded by Johannes Hahn
More info on projected rest of books, direct from Prof Solomon
Source Link
David Roberts
  • 33.2k
  • 10
  • 113
  • 316
Loading
Added reference to volume 9
Source Link
Timothy Chow
  • 76.9k
  • 24
  • 343
  • 556
Loading
Mar 2019 update.
Source Link
Nick Gill
  • 11.1k
  • 39
  • 69
Loading
Added details of projected volumes
Source Link
David Roberts
  • 33.2k
  • 10
  • 113
  • 316
Loading
added 219 characters in body
Source Link
David Roberts
  • 33.2k
  • 10
  • 113
  • 316
Loading
added 161 characters in body
Source Link
David Roberts
  • 33.2k
  • 10
  • 113
  • 316
Loading
Source Link
David Roberts
  • 33.2k
  • 10
  • 113
  • 316
Loading