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| title | chunk | source | category | tags | date_saved | instance |
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| Classification of finite simple groups | 4/4 | https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups | reference | science, encyclopedia | 2026-05-05T09:08:19.935542+00:00 | kb-cron |
== References == Aschbacher, Michael (2004). "The Status of the Classification of the Finite Simple Groups" (PDF). Notices of the American Mathematical Society. Vol. 51, no. 7. pp. 736–740. Aschbacher, Michael; Lyons, Richard; Smith, Stephen D.; Solomon, Ronald (2011), The Classification of Finite Simple Groups: Groups of Characteristic 2 Type, Mathematical Surveys and Monographs, vol. 172, ISBN 978-0-8218-5336-8 Conway, John Horton; Curtis, Robert Turner; Norton, Simon Phillips; Parker, Richard A; Wilson, Robert Arnott (1985), Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups, Oxford University Press, ISBN 978-0-19-853199-9 Gorenstein, D. (1979), "The classification of finite simple groups. I. Simple groups and local analysis", Bulletin of the American Mathematical Society, New Series, 1 (1): 43–199, doi:10.1090/S0273-0979-1979-14551-8, ISSN 0002-9904, MR 0513750 Gorenstein, D. (1982), Finite simple groups, University Series in Mathematics, New York: Plenum Publishing Corp., ISBN 978-0-306-40779-6, MR 0698782 Gorenstein, D. (1983), The classification of finite simple groups. Vol. 1. Groups of noncharacteristic 2 type, The University Series in Mathematics, Plenum Press, ISBN 978-0-306-41305-6, MR 0746470 Daniel Gorenstein (1985), "The Enormous Theorem", Scientific American, December 1, 1985, vol. 253, no. 6, pp. 104–115. Gorenstein, D. (1986), "Classifying the finite simple groups", Bulletin of the American Mathematical Society, New Series, 14 (1): 1–98, doi:10.1090/S0273-0979-1986-15392-9, ISSN 0002-9904, MR 0818060 Gorenstein, D.; Lyons, Richard; Solomon, Ronald (1994), The classification of the finite simple groups, Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0334-9, MR 1303592 Gorenstein, D.; Lyons, Richard; Solomon, Ronald (1996), The classification of the finite simple groups, Number 2, Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0390-5, MR 1358135 Gorenstein, D.; Lyons, Richard; Solomon, Ronald (1998), The classification of the finite simple groups, Number 3, Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0391-2, MR 1490581 Gorenstein, D.; Lyons, Richard; Solomon, Ronald (1999), The classification of the finite simple groups, Number 4. Part II, Chapters 1-4: Uniqueness Theorems, Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1379-9, MR 1675976 Gorenstein, D.; Lyons, Richard; Solomon, Ronald (2002), The classification of the finite simple groups, Number 5, Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-2776-5, MR 1923000 Gorenstein, D.; Lyons, Richard; Solomon, Ronald (2005), The classification of the finite simple groups, Number 6: Part IV: The Special Odd Case, Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-2777-2, MR 2104668 Gorenstein, D.; Lyons, Richard; Solomon, Ronald (2018), The classification of the finite simple groups, Number 7: Part III, Chapters 7–11: The Generic Case, Stages 3b and 4a, Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-4069-6, MR 3752626 Gorenstein, D.; Lyons, Richard; Solomon, Ronald (2018), The Classification of the Finite Simple Groups, Number 8: Part III, Chapters 12–17: The Generic Case, Completed, Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, ISBN 978-1-4704-4189-0, MR 3887657 Capdeboscq, Inna; Gorenstein, D.; Lyons, Richard; Solomon, Ronald (2021), The Classification of the Finite Simple Groups, Number 9: Part V, Chapters 1-8: Theorem
C
5
{\displaystyle C_{5}}
and Theorem
C
6
{\displaystyle C_{6}}
, Stage 1, Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, ISBN 978-1-4704-6437-0, MR 4244365 Capdeboscq, Inna; Gorenstein, D.; Lyons, Richard; Solomon, Ronald (2023), The Classification of the Finite Simple Groups, Number 10: Part V, Chapters 9-17: Theorem
C
6
{\displaystyle C_{6}}
and Theorem
C
4
∗
{\displaystyle C_{4}^{*}}
, Case A, Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, ISBN 978-1-4704-7553-6, MR 4656413 Mark Ronan, Symmetry and the Monster, ISBN 978-0-19-280723-6, Oxford University Press, 2006. (Concise introduction for lay reader) Marcus du Sautoy, Finding Moonshine, Fourth Estate, 2008, ISBN 978-0-00-721461-7 (another introduction for the lay reader. American edition published in 2009 as Symmetry: A Journey into the Patterns of Nature) Ron Solomon (1995) "On Finite Simple Groups and their Classification," Notices of the American Mathematical Society. (Not too technical and good on history. American version published in 2009 as Symmetry: A Journey into the Patterns of Nature) Solomon, Ronald (2001), "A brief history of the classification of the finite simple groups" (PDF), Bulletin of the American Mathematical Society, New Series, 38 (3): 315–352, doi:10.1090/S0273-0979-01-00909-0, ISSN 0002-9904, MR 1824893, archived (PDF) from the original on 2001-06-15 – article won Levi L. Conant prize for exposition Thompson, John G. (1984), "Finite nonsolvable groups", in Gruenberg, K. W.; Roseblade, J. E. (eds.), Group theory. Essays for Philip Hall, Boston, MA: Academic Press, pp. 1–12, ISBN 978-0-12-304880-6, MR 0780566 Wilson, Robert A. (2009), The finite simple groups, Graduate Texts in Mathematics 251, vol. 251, Berlin, New York: Springer-Verlag, doi:10.1007/978-1-84800-988-2, ISBN 978-1-84800-987-5, Zbl 1203.20012
== External links == ATLAS of Finite Group Representations. Searchable database of representations and other data for many finite simple groups. Elwes, Richard, "An enormous theorem: the classification of finite simple groups," Plus Magazine, Issue 41, December 2006. For laypeople. Madore, David (2003) Orders of nonabelian simple groups. Archived 2005-04-04 at the Wayback Machine Includes a list of all nonabelian simple groups up to order 1010. In what sense is the classification of all finite groups “impossible”? Ornes, Stephen (2015). "Researchers Race to Rescue the Enormous Theorem before Its Giant Proof Vanishes". Scientific American. 313 (1): 68–75. doi:10.1038/scientificamerican0715-68. PMID 26204718. "Where are the second- (and third-)generation proofs of the classification of finite simple groups up to?". MathOverflow. (Last updated in February 2024)