Afterword to the article “A brief history of the classification of the finite simple groups”

Solomon, Ron

doi:10.1090/bull/1639

Afterword to the article “A brief history of the classification of the finite simple groups”
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Bull. Amer. Math. Soc. 55 (2018), 453-457 Request permission

Abstract:

In this afterword the author discusses his previously published article “A brief history of the classification of the finite simple groups”, which appeared in Bull. Amer. Math. Soc. (N.S) 38 (2001), no. 3, 315–352.

References

Michael Aschbacher, Radha Kessar, and Bob Oliver, Fusion systems in algebra and topology, London Mathematical Society Lecture Note Series, vol. 391, Cambridge University Press, Cambridge, 2011. MR 2848834, DOI 10.1017/CBO9781139003841
Michael Aschbacher and Bob Oliver, Fusion systems, Bull. Amer. Math. Soc. (N.S.) 53 (2016), no. 4, 555–615. MR 3544261, DOI 10.1090/bull/1538
Michael Aschbacher and Stephen D. Smith, The classification of quasithin groups. I, Mathematical Surveys and Monographs, vol. 111, American Mathematical Society, Providence, RI, 2004. Structure of strongly quasithin $K$-groups. MR 2097623, DOI 10.1090/surv/111
Curtis D. Bennett and Sergey Shpectorov, A new proof of a theorem of Phan, J. Group Theory 7 (2004), no. 3, 287–310. MR 2062999, DOI 10.1515/jgth.2004.010
R. Blok, C. Hoffman and S. Shpectorov, Classification of Curtis-Tits and Phan amalgams with $3$-spherical diagram, Israel J. Math. (to appear).
Peter J. Cameron, Finite permutation groups and finite simple groups, Bull. London Math. Soc. 13 (1981), no. 1, 1–22. MR 599634, DOI 10.1112/blms/13.1.1
Andrew Chermak, Fusion systems and localities, Acta Math. 211 (2013), no. 1, 47–139. MR 3118305, DOI 10.1007/s11511-013-0099-5
Burton Fein, William M. Kantor, and Murray Schacher, Relative Brauer groups. II, J. Reine Angew. Math. 328 (1981), 39–57. MR 636194, DOI 10.1515/crll.1981.328.39
Michael D. Fried, Robert Guralnick, and Jan Saxl, Schur covers and Carlitz’s conjecture, Israel J. Math. 82 (1993), no. 1-3, 157–225. MR 1239049, DOI 10.1007/BF02808112
Robert M. Guralnick, Zeroes of permutation characters with applications to prime splitting and Brauer groups, J. Algebra 131 (1990), no. 1, 294–302. MR 1055010, DOI 10.1016/0021-8693(90)90177-P
George Glauberman and Justin Lynd, Control of fixed points and existence and uniqueness of centric linking systems, Invent. Math. 206 (2016), no. 2, 441–484. MR 3570297, DOI 10.1007/s00222-016-0657-5
Ralf Gramlich, Developments in finite Phan theory, Innov. Incidence Geom. 9 (2009), 123–175. MR 2658896, DOI 10.2140/iig.2009.9.123
Robert M. Guralnick, Joel Rosenberg, and Michael E. Zieve, A new family of exceptional polynomials in characteristic two, Ann. of Math. (2) 172 (2010), no. 2, 1361–1390. MR 2680493, DOI 10.4007/annals.2010.172.1367
Robert M. Guralnick and John Shareshian, Symmetric and alternating groups as monodromy groups of Riemann surfaces. I. Generic covers and covers with many branch points, Mem. Amer. Math. Soc. 189 (2007), no. 886, vi+128. With an appendix by Guralnick and R. Stafford. MR 2343794, DOI 10.1090/memo/0886
Robert M. Guralnick and Michael E. Zieve, Polynomials with $\textrm {PSL}(2)$ monodromy, Ann. of Math. (2) 172 (2010), no. 2, 1315–1359. MR 2680492, DOI 10.4007/annals.2010.172.1321
I. M. Isaacs, Gunter Malle, and Gabriel Navarro, A reduction theorem for the McKay conjecture, Invent. Math. 170 (2007), no. 1, 33–101. MR 2336079, DOI 10.1007/s00222-007-0057-y
Radha Kessar and Gunter Malle, Quasi-isolated blocks and Brauer’s height zero conjecture, Ann. of Math. (2) 178 (2013), no. 1, 321–384. MR 3043583, DOI 10.4007/annals.2013.178.1.6
Radha Kessar and Gunter Malle, Brauer’s height zero conjecture for quasi-simple groups, J. Algebra 475 (2017), 43–60. MR 3612463, DOI 10.1016/j.jalgebra.2016.05.010
U. Meierfrankenfeld, G. Parmeggiani, and B. Stellmacher, General offender theory, J. Algebra 495 (2018), 264–288. MR 3726111, DOI 10.1016/j.jalgebra.2017.11.005
Gunter Malle and Britta Späth, Characters of odd degree, Ann. of Math. (2) 184 (2016), no. 3, 869–908. MR 3549625, DOI 10.4007/annals.2016.184.3.6
Ulrich Meierfrankenfeld, Bernd Stellmacher, and Gernot Stroth, Finite groups of local characteristic $p$: an overview, Groups, combinatorics & geometry (Durham, 2001) World Sci. Publ., River Edge, NJ, 2003, pp. 155–192. MR 1994966, DOI 10.1142/9789812564481_{0}010
U. Meierfrankenfeld, B. Stellmacher, and G. Stroth, The local structure for finite groups with a large $p$-subgroup, Mem. Amer. Math. Soc. 242 (2016), no. 1147, vii+342. MR 3517155, DOI 10.1090/memo/1147
Ulrich Meierfrankenfeld, Gernot Stroth, and Richard M. Weiss, Local identification of spherical buildings and finite simple groups of Lie type, Math. Proc. Cambridge Philos. Soc. 154 (2013), no. 3, 527–547. MR 3044213, DOI 10.1017/S0305004113000078
Gabriel Navarro and Britta Späth, On Brauer’s height zero conjecture, J. Eur. Math. Soc. (JEMS) 16 (2014), no. 4, 695–747. MR 3191974, DOI 10.4171/JEMS/444
Bob Oliver, Equivalences of classifying spaces completed at odd primes, Math. Proc. Cambridge Philos. Soc. 137 (2004), no. 2, 321–347. MR 2092063, DOI 10.1017/S0305004104007728
Bob Oliver, Equivalences of classifying spaces completed at the prime two, Mem. Amer. Math. Soc. 180 (2006), no. 848, vi+102. MR 2203209, DOI 10.1090/memo/0848
Stephen D. Smith, Applying the classification of finite simple groups, Mathematical Surveys and Monographs, vol. 230, American Mathematical Society, Providence, RI, 2018. A user’s guide. MR 3753581, DOI 10.1090/surv/230
R. Solomon, The classification of finite simple groups: a progress report, Notices Amer. Math. Soc. 65 (2018), no. 6, 646–651.
Britta Späth, A reduction theorem for the Alperin-McKay conjecture, J. Reine Angew. Math. 680 (2013), 153–189. MR 3100954, DOI 10.1515/crelle.2012.035
Pham Huu Tiep, Representation of finite groups: conjectures, reductions, and applications, Acta Math. Vietnam. 39 (2014), no. 1, 87–109. MR 3176464, DOI 10.1007/s40306-013-0043-y