Volume 7, issue 4 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Chevalley $p$–local finite groups

Carles Broto and Jesper M Møller

Algebraic & Geometric Topology 7 (2007) 1809–1919
Bibliography
1 J Aguadé, Constructing modular classifying spaces II, unpublished manuscript
2 J Aguadé, Constructing modular classifying spaces, Israel J. Math. 66 (1989) 23 MR1017153
3 J Aguadé, L Smith, Modular cohomology algebras, Amer. J. Math. 107 (1985) 507 MR789653
4 J L Alperin, P Fong, Weights for symmetric and general linear groups, J. Algebra 131 (1990) 2 MR1054996
5 K K S Andersen, The normalizer splitting conjecture for $p$–compact groups, Fund. Math. 161 (1999) 1 MR1713198
6 K K S Andersen, J Grodal, The classification of 2–compact groups, preprint
7 K K S Andersen, J Grodal, J M Møller, A Viruel, The classification of $p$–compact groups for $p$ odd, Ann. of Math. (to appear)
8 M Aubry, Homotopy theory and models, DMV Seminar 24, Birkhäuser Verlag (1995) MR1347447
9 D J Benson, Cohomology of sporadic groups, finite loop spaces, and the Dickson invariants, from: "Geometry and cohomology in group theory (Durham, 1994)" (editors P H Kropholler, G A Niblo, R Stöhr), London Math. Soc. Lecture Note Ser. 252, Cambridge Univ. Press (1998) 10 MR1709949
10 A K Bousfield, The localization of spaces with respect to homology, Topology 14 (1975) 133 MR0380779
11 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. 304, Springer (1972) MR0365573
12 C Broto, Caràcters lineals i fibracions esfèriques (Catalan), PhD thesis, Universitat Autònoma de Barcelona (1988)
13 C Broto, R Levi, B Oliver, Homotopy equivalences of $p$–completed classifying spaces of finite groups, Invent. Math. 151 (2003) 611 MR1961340
14 C Broto, R Levi, B Oliver, The homotopy theory of fusion systems, J. Amer. Math. Soc. 16 (2003) 779 MR1992826
15 C Broto, R Levi, B Oliver, The theory of $p$–local groups: a survey, from: "Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic $K$–theory" (editors P Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 51 MR2066496
16 C Broto, J M Møller, Embeddings of $\mathrm{DI}_2$ in $F_4$, Trans. Amer. Math. Soc. 353 (2001) 4461 MR1851179
17 C Broto, L Smith, R Stong, Thom modules and pseudoreflection groups, J. Pure Appl. Algebra 60 (1989) 1 MR1014604
18 N Castellana, Quillen Grassmannians as non-modular homotopy fixed points, Math. Z. 248 (2004) 477 MR2097370
19 A Clark, J Ewing, The realization of polynomial algebras as cohomology rings, Pacific J. Math. 50 (1974) 425 MR0367979
20 W G Dwyer, The centralizer decomposition of $BG$, from: "Algebraic topology: new trends in localization and periodicity (Sant Feliu de Guíxols, 1994)" (editors C Broto, C Casacuberta, G Mislin), Progr. Math. 136, Birkhäuser (1996) 167 MR1397728
21 W G Dwyer, Lie groups and $p$–compact groups, from: "Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998)" (1998) 433 MR1648093
22 W G Dwyer, Sharp homology decompositions for classifying spaces of finite groups, from: "Group representations: cohomology, group actions and topology (Seattle, WA, 1996)" (editors A Adem, J Carlson, S Priddy, P Webb), Proc. Sympos. Pure Math. 63, Amer. Math. Soc. (1998) 197 MR1603159
23 W G Dwyer, H R Miller, C W Wilkerson, Homotopical uniqueness of classifying spaces, Topology 31 (1992) 29 MR1153237
24 W G Dwyer, C W Wilkerson, A new finite loop space at the prime two, J. Amer. Math. Soc. 6 (1993) 37 MR1161306
25 W G Dwyer, C W Wilkerson, Homotopy fixed-point methods for Lie groups and finite loop spaces, Ann. of Math. $(2)$ 139 (1994) 395 MR1274096
26 W G Dwyer, C W Wilkerson, The center of a $p$–compact group, from: "The Čech centennial (Boston, 1993)", Contemp. Math. 181, Amer. Math. Soc. (1995) 119 MR1320990
27 W G Dwyer, C W Wilkerson, Product splittings for $p$–compact groups, Fund. Math. 147 (1995) 279 MR1348723
28 W G Dwyer, C W Wilkerson, Kähler differentials, the $T$–functor, and a theorem of Steinberg, Trans. Amer. Math. Soc. 350 (1998) 4919 MR1621741
29 E D Farjoun, Cellular spaces, null spaces and homotopy localization, Lecture Notes in Math. 1622, Springer (1996) MR1392221
30 Z Fiedorowicz, S Priddy, Homology of classical groups over a finite field, from: "Algebraic $K$–theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976)", Lecture Notes in Math. 551, Springer (1976) 269 MR0500958
31 Z Fiedorowicz, S Priddy, Homology of classical groups over finite fields and their associated infinite loop spaces, Lecture Notes in Math. 674, Springer (1978) MR513424
32 E M Friedlander, Exceptional isogenies and the classifying spaces of simple Lie groups, Ann. Math. $(2)$ 101 (1975) 510 MR0391078
33 E M Friedlander, Unstable $K$–theories of the algebraic closure of a finite field, Comment. Math. Helv. 50 (1975) 145 MR0410742
34 E M Friedlander, Étale homotopy of simplicial schemes, Annals of Mathematics Studies 104, Princeton University Press (1982) MR676809
35 D Gorenstein, Finite groups, Chelsea Publishing Co. (1980) MR569209
36 J R Harper, The $\mathrm{mod} 3$ homotopy type of $F_4$, from: "Localization in group theory and homotopy theory, and related topics (Sympos., Battelle Seattle Res. Center, Seattle, Wash., 1974)" (editor P Hilton), Lecture Notes in Math. 418, Springer (1974) 58 MR0365558
37 B Harris, Suspensions and characteristic maps for symmetric spaces, Ann. of Math. $(2)$ 76 (1962) 295 MR0149479
38 S Jackowski, J McClure, B Oliver, Self-homotopy equivalences of classifying spaces of compact connected Lie groups, Fund. Math. 147 (1995) 99 MR1341725
39 S N Kleinerman, The cohomology of Chevalley groups of exceptional Lie type, Mem. Amer. Math. Soc. 39 (1982) MR668808
40 R Levi, B Oliver, Construction of 2–local finite groups of a type studied by Solomon and Benson, Geom. Topol. 6 (2002) 917 MR1943386
41 M W Liebeck, J Saxl, G M Seitz, Subgroups of maximal rank in finite exceptional groups of Lie type, Proc. London Math. Soc. $(3)$ 65 (1992) 297 MR1168190
42 S Mac Lane, Homology, Classics in Mathematics, Springer (1995) MR1344215
43 G Malle, The maximal subgroups of ${}^2F_4(q^2)$, J. Algebra 139 (1991) 52 MR1106340
44 M Mimura, G Nishida, H Toda, $\mathrm{Mod} p$ decomposition of compact Lie groups, Publ. Res. Inst. Math. Sci. 13 (1977/78) 627 MR0478187
45 M Mimura, M. Tezuka, S. Tsukuda, On the cohomology of finite Chevalley groups, in preparation
46 M Mimura, H Toda, Topology of Lie groups I, II, Translations of Mathematical Monographs 91, American Mathematical Society (1991) MR1122592
47 J M Møller, Spaces of sections of Eilenberg–Mac Lane fibrations, Pacific J. Math. 130 (1987) 171 MR910659
48 J M Møller, Homotopy Lie groups, Bull. Amer. Math. Soc. $($N.S.$)$ 32 (1995) 413 MR1322786
49 J M Møller, Extensions of $p$–compact groups, from: "Algebraic topology: new trends in localization and periodicity (Sant Feliu de Guíxols, 1994)" (editors C Broto, C Casacuberta, G Mislin), Progr. Math. 136, Birkhäuser (1996) 307 MR1397740
50 J M Møller, Rational isomorphisms of $p$–compact groups, Topology 35 (1996) 201 MR1367281
51 J M Møller, Deterministic $p$–compact groups, from: "Stable and unstable homotopy (Toronto, ON, 1996)", Fields Inst. Commun. 19, Amer. Math. Soc. (1998) 255 MR1622352
52 J M Møller, Normalizers of maximal tori, Math. Z. 231 (1999) 51 MR1696756
53 J M Møller, $N$–determined $p$–compact groups, Fund. Math. 173 (2002) 201 MR1925483
54 J M Møller, $N$–determined 2–compact groups I, Fund. Math. 195 (2007) 11 MR2314074
55 J M Møller, D Notbohm, Connected finite loop spaces with maximal tori, Trans. Amer. Math. Soc. 350 (1998) 3483 MR1487627
56 H Mui, Modular invariant theory and cohomology algebras of symmetric groups, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 22 (1975) 319 MR0422451
57 D Notbohm, Classifying spaces of compact Lie groups and finite loop spaces, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 1049 MR1361906
58 D Notbohm, Topological realization of a family of pseudoreflection groups, Fund. Math. 155 (1998) 1 MR1487985
59 D Notbohm, Unstable splittings of classifying spaces of $p$–compact groups, Q. J. Math. 51 (2000) 237 MR1765793
60 L Puig, Frobenius categories, J. Algebra 303 (2006) 309 MR2253665
61 D Quillen, On the cohomology and $K$–theory of the general linear groups over a finite field, Ann. of Math. $(2)$ 96 (1972) 552 MR0315016
62 J P Serre, Cohomologie galoisienne, Lecture Notes in Math. 5, Springer (1994) MR1324577
63 G C Shephard, J A Todd, Finite unitary reflection groups, Canadian J. Math. 6 (1954) 274 MR0059914
64 L Smith, On the realization and classification of symmetric algebras as cohomology rings, Proc. Amer. Math. Soc. 87 (1983) 144 MR677250
65 R Solomon, Finite groups with Sylow 2–subgroups of type 3, J. Algebra 28 (1974) 182 MR0344338
66 J D Stasheff, The $\mathrm{mod} p$ decomposition of Lie groups, from: "Localization in group theory and homotopy theory, and related topics (Sympos., Battelle Seattle Res. Center, Seattle, Wash., 1974)" (editor P Hilton), Lecture Notes in Math. 418, Springer (1974) 142 MR0375294
67 D P Sullivan, Geometric topology: localization, periodicity and Galois symmetry, K–Monographs in Mathematics 8, Springer (2005) MR2162361
68 C W Wilkerson, Self-maps of classifying spaces, from: "Localization in group theory and homotopy theory, and related topics (Sympos., Battelle Seattle Res. Center, Seattle, Wash., 1974)" (editor P Hilton), Lecture Notes in Math. 418, Springer (1974) 150 MR0383444
69 C W Wilkerson, Rings of invariants and inseparable forms of algebras over the Steenrod algebra, from: "Recent progress in homotopy theory (Baltimore, MD, 2000)" (editors D M Davis, J Morava, G Nishida, W S Wilson, N Yagita), Contemp. Math. 293, Amer. Math. Soc. (2002) 381 MR1890745
70 C Xu, Computing invariant polynomials of $p$–adic reflection groups, from: "Mathematics of Computation 1943–1993: a half-century of computational mathematics (Vancouver, BC, 1993)" (editor W Gautschi), Proc. Sympos. Appl. Math. 48, Amer. Math. Soc. (1994) 599 MR1314898
71 A Zabrodsky, On the realization of invariant subgroups of $\pi_{*}(X)$, Trans. Amer. Math. Soc. 285 (1984) 467 MR752487