The Morava -theories of some classifying spaces

Author:
Nicholas J. Kuhn

Journal:
Trans. Amer. Math. Soc. **304** (1987), 193-205

MSC:
Primary 55N22; Secondary 19L99

DOI:
https://doi.org/10.1090/S0002-9947-1987-0906812-8

MathSciNet review:
906812

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite abelian -group with classifying space . We compute, in representation theoretic terms, the Morava -theories of the stable wedge summands of . In particular, we obtain a simple, and purely group theoretic, description of the rank of for any finite group with an abelian -Sylow subgroup. A minimal amount of topology quickly reduces the problem to an algebraic one of analyzing truncated polynomial algebras as modular representations of the semigroup .

**[1]**J. F. Adams, J. H. Gunawardena and H. Miller,*The Segal conjecture for elementary abelian*-*groups*, Topology**24**(1985), 435-460. MR**816524 (87m:55026)****[2]**M. F. Atiyah,*Characters and cohomology of finite groups*, Publ. Math. Inst. Hautes Etudes Sci.**9**(1961), 247-288. MR**0148722 (26:6228)****[3]**D. Carlisle, P. Eccles, S. Hilditch, N. Ray, L. Schwartz, G. Walker and R. Wood,*Modular representations of*,*splitting*,*and the*-*family as framed hypersurfaces*, Math. Z.**189**(1985), 239-261. MR**779220 (86i:55021)****[4]**D. J. Glover,*A study of certain modular representations*, J. Algebra**51**(1978), 425-475. MR**0476841 (57:16392)****[5]**J. C. Harris and N. J. Kuhn,*Stable decompositions of classifying spaces of finite abelian*-*groups*, Math. Proc. Cambridge Philos. Soc. (submitted).**[6]**M. J. Hopkins and J. H. Smith,*Nilpotence and stable homotopy theory*. II (in preparation).**[7]**N. J. Kuhn,*The mod p*-*theory of classifying spaces of finite groups*, J. Pure Appl. Algebra**44**(1987), 269-271. MR**885110 (88g:55008)****[8]**N. J. Kuhn,*The rigidity of*, Proc. Topology year at Univ. of Washington (to appear).**[9]**N. J. Kuhn and S. B. Priddy,*The transfer and Whitehead's conjecture*, Math. Proc. Cambridge Philos. Soc.**98**(1985), 459-480. MR**803606 (87g:55030)****[10]**S. A. Mitchell,*Finite complexes with*-*free cohomology*, Topology**24**(1985), 227-248. MR**793186 (86k:55007)****[11]**D. G. Quillen,*On the associated graded ring of a group ring*, J. Algebra**10**(1968), 411-418. MR**0231919 (38:245)****[12]**D. C. Ravenel,*Morava*-*theories and finite groups*, Symposium on Algebraic Topology in Honor of José Adem, Contemp. Math., vol. 12, Amer. Math. Soc., Providence, R. I., 1982, pp. 289-292. MR**676336 (83m:55009)****[13]**D. C. Ravenel and W. S. Wilson,*The Morava*-*theories of Eilenberg-Mac Lane spaces and the Conner-Floyd conjecture*, Amer. J. Math.**102**(1980), 691-748. MR**584466 (81i:55005)****[14]**P. J. Welcher,*Symmetric fiber spectra and*-*homology acyclicity*, Indiana J. Math.**39**(1981), 801-812. MR**632853 (82m:55012)****[15]**N. J. Kuhn,*Morova*-*theories and infinite loop spaces*, Proc. 1986 Arcata Topology Conference (to appear).

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
55N22,
19L99

Retrieve articles in all journals with MSC: 55N22, 19L99

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1987-0906812-8

Article copyright:
© Copyright 1987
American Mathematical Society