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Stable decompositions of classifying spaces of finite abelian p-groups

Published online by Cambridge University Press:  24 October 2008

John C. Harris  and
Nicholas J. Kuhn
John C. Harris
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA, U.S.A.
Nicholas J. Kuhn
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, VA, U.S.A.
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Extract

Let BG be the classifying space of a finite group G. Consider the problem of finding a stable decomposition

into indecomposable wedge summands. Such a decomposition naturally splits E*(BG), where E* is any cohomology theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 3 , May 1988 , pp. 427 - 449
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Adams, J. F.. Infinite Loop Spaces. Annals of Math. Study no. 90 (Princeton University Press, 1978).CrossRefGoogle Scholar
[2]Adams, J. F., Gunawakdena, J. H. and Miller, H. R.. The Segal conjecture for elementary abelian p-groups. Topology 24 (1985), 435–460.CrossRefGoogle Scholar
[3]Carlisle, D.. Ph.D. thesis, University of Manchester (1985).Google Scholar
[4]Carlisle, D., private correspondence.Google Scholar
[5]Carlisle, D. and Kuhn, N. J.. Subalgebras of the Steenrod algebra and the action of matrices on truncated polynomial algebras. J. Algebra, to appear.Google Scholar
[6]Carlisle, D. and Kuhn, N. J.. Some smash product decompositions (in preparation).Google Scholar
[7]Carlsson, G.. Equivariant stable homotopy and Segal's Burnside ring conjecture. Ann. of Math. (2) 120 (1984), 189–224.CrossRefGoogle Scholar
[8]Clifford, A. H. and Preston, G. B.. Algebraic Theory of Semigroups, Vol. 1. Math. Surveys of the A.M.S. no. 7, (1961).CrossRefGoogle Scholar
[9]Curtis, C. W. and Reiner, I.. Methods of Representation Theory vol. I, (Wiley, 1981).Google Scholar
[10]Glover, D. J.. A study of certain modular representations. J. Algebra 51 (1978), 425–475.Google Scholar
[11]Harris, J. C.. Ph.D. thesis, University of Chicago (1985).Google Scholar
[12]Howie, J. M.. An Introduction to Semigroup Theory (Academic Press, 1976).Google Scholar
[13]Humphreys, J. E.. Ordinary and modular characters of SL (3, p). J. Algebra, 72 (1981), 8–16.CrossRefGoogle Scholar
[14]Huppert, B.. Endliche Gruppen I (Springer-Verlag, 1967).Google Scholar
[15]James, G. and Kerber, A.. The Representation Theory of the Symmetric Group. Encyclopedia of Math., vol. 16 (Addison-Wesley, 1981).Google Scholar
[16]Kuhn, N. J.. Suspension spectra and homology equivalences. Trans. Amer. Math. Soc. 283 (1984), 303–313.Google Scholar
[17]Kuhn, N. J.. The Morava K-theory of some classifying spaces. Trans Amer. Math. Soc. 304 (1987), 193–205.Google Scholar
[18]Kuhn, N. J.. The rigidity of L(n). In Algebraic Topology – Proceedings, Seattle 1985, Lecture Notes in Math. vol. 1286 (Springer-Verlag 1987), pp. 286–292.Google Scholar
[19]Lallemont, G. and Petrich, M.. Irreducible matrix representations of finite semigroups. Trans Amer. Math. Soc. 139 (1969), 392–412.Google Scholar
[20]Landrock, P.. Finite Group Algebras and their Modules. London Math. Soc. Lecture Note Series no. 84 (Cambridge University Press, 1983).Google Scholar
[21]Lannes, J. and Schwartz, L.. On the structure of the -injectives. Preprint.Google Scholar
[22]May, J. P.. Stable maps between classifying spaces. Amer. Math. Soc. Cont. Math. 37 (1985), 121–129.Google Scholar
[23]Mitchell, S. A. and Priddy, S. B.. Symmetric product spectra and splittings of classifying spaces. Amer. J. Math. 106 (1984), 219–232.Google Scholar
[24]Mitchell, S. A. and Priddy, S. B.. Stable splittings derived from the Steinberg module. Topology 22 (1983), 285–298.Google Scholar
[25]Mitchell, S. A.. Splitting B(ℤ/p)n and BT n via modular representation theory. Math. Z. 189 (1985), 1–9.Google Scholar
[26]Nishida, G.. Stable homotopy type of classifying spaces of finite groups. Preprint (1985).Google Scholar
[27]Rotman, J. J., The Theory of Groups (Allyn and Bacon, 1973).Google Scholar
[28]Serre, J. P.. Linear Representation of Finite Groups. Graduate Texts in Math. vol. 42 (Springer-Verlag, 1977).Google Scholar
[29]Steinberg, R.. Lectures on Chevalley Groups. Yale Lecture Notes (1967).Google Scholar
[30]Swan, R.. The p-period of a finite group. Illinois J. Math. 4 (1960), 341–346.Google Scholar
[31]Schwartz, L.. (In preparation.)Google Scholar
[32]Toda, H.. p-primary components of homotopy groups IV. Mem. Coll. See. Kyoto, Series A 32 (1959), 297–332.Google Scholar