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Abstract

In the beginning of 1980's Cohen, R. proved thath0b(1k)=B(1,k)=B(1,k)⊗ζ1 survives toE in the Adams spectral sequence. Later, Cohen, R. and Goerss, P. proved that is a permanent cycle. And they are represented by ζ k j respectively. Here the author proved: Theorem 2: Let 2≤sp−1,j≥3, then β s η j ≠0. Theorem 3: For 2≤sp−1,k≥2, β s ζ k ≠0 in the stable homotopy groups of spheres.
As a remark, we get bs bpk /pk - 1 ¹ 0\beta _s \beta _{p^k /p^k - 1} \ne 0 in ExtB P*BP*,* (BP*,BP*)Ext_{B P*BP}^{*,*} (BP*,BP*) .
Supported by Doctoral Program Fundation.

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