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On the Segal conjecture for $ Z\sb{2}\times Z\sb{2}$


Author: Donald M. Davis
Journal: Proc. Amer. Math. Soc. 83 (1981), 619-622
MSC: Primary 55Q55; Secondary 55T15
DOI: https://doi.org/10.1090/S0002-9939-1981-0627705-X
MathSciNet review: 627705
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Abstract: The Segal conjecture regarding the Burnside ring and stable cohomotopy of a finite group $ G$ is reduced for the case $ G = {Z_2} \times {Z_2}$ to a statement about Ext groups. This statement has since been proved by H. Miller, J. F. Adams and J. H. C. Gonawardena.


References [Enhancements On Off] (What's this?)

  • [1] D. M. Davis, On the Segal conjecture for $ {Z_2} \times {Z_2}$, Lecture at Oberwolfach Homotopy Theory Conf., Sept., 1980.
  • [2] J. H. C. Gunawardena, Segal's conjecture for cyclic groups of odd prime order, J. T. Knight Prize Essay, Cambridge, 1980.
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  • [5] W. H. Lin, D. M. Davis, M. Mahowald and J. F. Adams, Calculation of Lin's Ext groups, Math. Proc. Cambridge Philos. Soc. 87 (1980), 459-469. MR 569195 (81e:55025)
  • [6] H. Miller, An algebraic analogue of a conjecture of G. W. Whitehead (to appear). MR 633294 (83c:55026)
  • [7] J. F. Adams, J. H. C. Gunawardena and H. Miller, The Segal conjecture for $ {({Z_2})^n}$ (to appear).
  • [8] S. B. Priddy, On $ {\Omega ^\infty }{S^\infty }$ and the infinite symmetric group, Proc. Sympos. Pure Math., vol. 22, Amer. Math. Soc., Providence, R.I., 1971, pp. 217-220. MR 0358767 (50:11226)
  • [9] D. C. Ravenel, The Segal conjecture for cyclic groups, Bull. London Math. Soc. 13 (1981), 42-44. MR 599639 (82e:55017)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0627705-X
Keywords: Segal conjecture, stable cohomotopy groups, Burnside ring
Article copyright: © Copyright 1981 American Mathematical Society

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