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On the nilpotence order of β1

Published online by Cambridge University Press:  24 October 2008

Chun-Nip Lee  and
Douglas C. Ravenel
Chun-Nip Lee
Affiliation:
Department of Mathematics, Northwestern University, Evanston, Illinois 60208, USA
Douglas C. Ravenel
Affiliation:
Department of Mathematics, University of Rochester, River Station Road, Rochester, NY 14627, USA
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Extract

For p > 2, is the first positive even-dimensional element in the stable homotopy groups of spheres. A classical theorem of Nishida[1] states that all elements of positive dimension in the stable homotopy groups of spheres are nilpotent. In fact, Toda [4] proved . For p = 3 he showed that while . In [2] the second author computed the first thousand stems of the stable homotopy groups of spheres at the prime 5. One of the consequences of this computation is that while .

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 3 , May 1994 , pp. 483 - 488
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

REFERENCES

[1]Nishida, G.. The nilpotence of elements of the stable homotopy groups of spheres. J. Math. Soc. of Japan 25 (1973), 707–732.Google Scholar
[2]Ravenel, D. C.. Complex Cobordism and Stable Homotopy Groups of Spheres (Academic Press, 1986).Google Scholar
[3]Smith, L.. On realizing complex cobordism modules. IV. Applications to the stable homotopy groups of spheres. Amer. J. Math. 99 (1971), 418–436.CrossRefGoogle Scholar
[4]Toda, H.. Extended p-th powers of complexes and applications to homotopy theory. Proc. Jap. Acad. 44 (1968), 198–203.Google Scholar
[5]Toda, H.. On spectra realizing exterior parts of the Steenrod algebra. Topology 10 (1971), 53–65.CrossRefGoogle Scholar