In the beginning of 1980's Cohen, R. proved that
h0
b(1
k)=
B(1,
k)=
B(1,
k)⊗ζ
1 survives to
E
∞ in the Adams spectral sequence. Later, Cohen, R. and Goerss, P. proved that is a permanent cycle. And they are represented
by ζ
k
,η
j respectively. Here the author proved: Theorem 2: Let 2≤
s≤
p−1,
j≥3, then β
s
η
j
≠0. Theorem 3: For 2≤
s≤
p−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.