Book Review
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MathSciNet review:
2791779
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Book Information:
Authors:
David J. Benson and
Stephen D. Smith
Title:
Classifying spaces of sporadic groups
Additional book information:
Mathematical Surveys and Monographs 147,
American Mathematical Society, Providence, RI,
2008,
xvi + 289 pp.,
ISBN 978-0-8218-4474-8
Michael Aschbacher and Yoav Segev, Uniqueness of sporadic groups, Groups, combinatorics & geometry (Durham, 1990) London Math. Soc. Lecture Note Ser., vol. 165, Cambridge Univ. Press, Cambridge, 1992, pp. 1–11. MR 1200245, DOI 10.1017/CBO9780511629259.003
Michael Aschbacher and Yoav Segev, Extending morphisms of groups and graphs, Ann. of Math. (2) 135 (1992), no. 2, 297–323. MR 1154595, DOI 10.2307/2946591
D. J. Benson, Representations and cohomology. II, Cambridge Studies in Advanced Mathematics, vol. 31, Cambridge University Press, Cambridge, 1991. Cohomology of groups and modules. MR 1156302
David J. Benson and Stephen D. Smith, Classifying spaces of sporadic groups, Mathematical Surveys and Monographs, vol. 147, American Mathematical Society, Providence, RI, 2008. MR 2378355, DOI 10.1090/surv/147
Serge Bouc, Homologie de certains ensembles ordonnés, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 2, 49–52 (French, with English summary). MR 756517
Francis Buekenhout, Diagrams for geometries and groups, J. Combin. Theory Ser. A 27 (1979), no. 2, 121–151. MR 542524, DOI 10.1016/0097-3165(79)90041-4
W. G. Dwyer, Homology decompositions for classifying spaces of finite groups, Topology 36 (1997), no. 4, 783–804. MR 1432421, DOI 10.1016/S0040-9383(96)00031-6
W. G. Dwyer, Sharp homology decompositions for classifying spaces of finite groups, Group representations: cohomology, group actions and topology (Seattle, WA, 1996) Proc. Sympos. Pure Math., vol. 63, Amer. Math. Soc., Providence, RI, 1998, pp. 197–220. MR 1603159, DOI 10.1090/pspum/063/1603159
Jesper Grodal, Higher limits via subgroup complexes, Ann. of Math. (2) 155 (2002), no. 2, 405–457. MR 1906592, DOI 10.2307/3062122
Jesper Grodal and Stephen D. Smith, Propagating sharp group homology decompositions, Adv. Math. 200 (2006), no. 2, 525–538. MR 2200855, DOI 10.1016/j.aim.2005.01.006
A. A. Ivanov, Geometry of sporadic groups. I, Encyclopedia of Mathematics and its Applications, vol. 76, Cambridge University Press, Cambridge, 1999. Petersen and tilde geometries. MR 1705272, DOI 10.1017/CBO9780511525933
Daniel Quillen, Homotopy properties of the poset of nontrivial $p$-subgroups of a group, Adv. in Math. 28 (1978), no. 2, 101–128. MR 493916, DOI 10.1016/0001-8708(78)90058-0
M. A. Ronan and S. D. Smith, $2$-local geometries for some sporadic groups, The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979) Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., 1980, pp. 283–289. MR 604595
Masato Sawabe, $2$-radical subgroups of the Conway simple group $\textrm {Co}_1$, J. Algebra 211 (1999), no. 1, 115–133. MR 1656574, DOI 10.1006/jabr.1998.7573
Masato Sawabe, The centric $p$-radical complex and a related $p$-local geometry, Math. Proc. Cambridge Philos. Soc. 133 (2002), no. 3, 383–398. MR 1919712, DOI 10.1017/S0305004102006175
Louis Solomon, The Steinberg character of a finite group with $BN$-pair, Theory of Finite Groups (Symposium, Harvard Univ., Cambridge, Mass., 1968), Benjamin, New York, 1969, pp. 213–221. MR 0246951
J. Tits, Les groupes de Lie exceptionnels et leur interprétation géométrique, Bull. Soc. Math. Belg. 8 (1956), 48–81 (French). MR 87889
P. J. Webb, A split exact sequence of Mackey functors, Comment. Math. Helv. 66 (1991), no. 1, 34–69. MR 1090164, DOI 10.1007/BF02566635
References
- M. Aschbacher and Y. Segev, Uniqueness of sporadic groups, Groups, combinatorics and geometry (Durham, 1990), London Math. Soc. Lecture Note Ser. 165, Cambridge Univ. Press (1992), 1–11. MR 1200245 (94e:20021)
- M. Aschbacher and Y. Segev, Extending morphisms of groups and graphs, Annals of Math. 135 (1992), 297–323. MR 1154595 (93d:20034)
- D. Benson, Representations and cohomology II: cohomology of groups and modules, Cambridge Univ. Press (1991). MR 1156302 (93g:20099)
- D. Benson and S. Smith, Classifying spaces of sporadic groups, Mathematical Surveys & Monographs 147, Amer. Math. Soc. (2008). MR 2378355 (2009f:55017)
- S. Bouc, Homologie de certains ensembles ordonnés, Comptes Rendus Acad. Sci. Paris Série I 299 (1984), 49–52. MR 756517 (85k:20150)
- F. Buekenhout, Diagrams for geometries and groups, J. Combin. Theory Ser. A 27 (1979), 121–151. MR 542524 (83f:51003)
- W. Dwyer, Homology decompositions for classifying spaces of finite groups, Topology 36 (1997), 783–804. MR 1432421 (97m:55016)
- W. Dwyer, Sharp homology decompositions for classifying spaces of finite groups, Proc. Symp. Pure Math. 63, Amer. Math. Soc. (1998), 197–220. MR 1603159 (99b:55033)
- J. Grodal, Higher limits via subgroup complexes, Annals of Math. 155 (2002), 405–457. MR 1906592 (2003g:55025)
- J. Grodal and S. Smith, Propagating sharp homology decompositions, Advances in Math. 200 (2006), 525–538. MR 2200855 (2007e:20110)
- A. Ivanov, The geometry of sporadic groups, I: Petersen and tilde geometries, Encyclopedia of Mathematics and Its Applications 76, Cambridge Univ. Press (1999). MR 1705272 (2000i:20028)
- D. Quillen, Homotopy properties of the poset of nontrivial $p$-subgroups of a finite group, Adv. in Math. 28 (1978), 101–128. MR 493916 (80k:20049)
- M. Ronan and S. Smith, 2-local geometries for some sporadic groups, Santa Cruz Conference on Finite Groups, Proc. Symp. Pure Math. 37, American Math. Soc. (1980), 283–289. MR 604595 (82c:20033)
- M. Sawabe, 2-radical subgroups of the Conway simple group $Co_1$, J. Algebra 211 (1999), 115–133. MR 1656574 (99k:20038)
- M. Sawabe, The centric $p$-radical complex and a related $p$-local geometry, Math. Proc. Camb. Phil. Soc. 133 (2002), 383–398. MR 1919712 (2003m:20014)
- L. Solomon, The Steinberg character of a finite group with a $BN$-pair, Theory of Finite Groups, Benjamin (1969), 213–221. MR 0246951 (40:220)
- J. Tits, Les groupes de Lie exceptionnels et leur interpretation geometrique, Bull. Soc. Math. Belg. 8 (1956), 48–81. MR 0087889 (19:430d)
- P. Webb, A split exact sequence of Mackey functors, Comment. Math. Helv. 66 (1991), 34–69. MR 1090164 (92c:20095)
Review Information:
Reviewer:
Bob Oliver
Affiliation:
LAGA, Institut Galilée, Université Paris 13, France
Email:
bobol@math.univ-paris13.fr
Journal:
Bull. Amer. Math. Soc.
48 (2011), 307-313
DOI:
https://doi.org/10.1090/S0273-0979-2010-01327-6
Published electronically:
November 30, 2010
Review copyright:
© Copyright 2010
American Mathematical Society
