By a method improving that of [1],the authors prove the existence of a nontrivial product of filtration,s+6,in the stable homotopy groups of sphere,πt-6S,which is represented up to non-zero scalar by βs+2h0(hmbn-1-hnbm-1) ∈ ExtsA+ 6,t+s(Zp,Zp) in the Adams spectral sequence,where p ≥ 7,n ≥ m+2 ≥ 5,q=2(p-1),0 ≤s< p-2,t =(s+2+(s+2)p+pm+pn)q. The advantage of this method is to extend the range of s without much complicated argument as in [1].
In this paper,we introduce a four-filtrated version of the May spectral sequence（MSS）,from which we study the general properties of the spectral sequence and give a collapse theorem.Wealso give an efficient method to detect generators of May E1-term E1s,t,b,*for a given（s,t,b,*）.As anapplication,we give a method to prove the non-triviality of some compositions of the known homotopyelements in the classical Adams spectral sequence（ASS）.
Xiu Gui LIU Xiang Jun WANG School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,P.R.China
让 A 现代派的 p Steenrod 代数学和 S 是在奇怪的主要 p 局部性的范围光谱。决定范围 π
* S 是在 homotopy 的中央问题之一理论。这篇论文在具有顺序 p 并且被 k 0 h n ∈(ℤ
p，在亚当斯的 ℤp ) 光谱顺序，在此 p ≥
5 是一个奇怪的素数， n ≥
3 并且 q = 2 (p −
1 ) 。在证明期间，在哪个被 β
*i′* i *(h n )∈
(H * V (1 ) ，在亚当斯顺序的 ℤ
p ) 被检测。
