中文摘要：

令p〉5是素数,A表示模p Steenrod代数,S表示球谱的P局部化.首先给出了有关May谱序列的一些重要定理,然后作为应用,利用May谱序列和Adams谱序列发觉了一族新的非零的球面稳定元素.该新元素族次数为2（p-1）（p^n＋sp^2＋sp＋s）-7,在Adams谱序列中由bn-190γ^^s∈Ext A^s＋4,＊（Zp,Zp）所表示,其中n≥4,3≤sP-2．该文的主要定理是文献[1]中的定理I的一个推广．

英文摘要：

　Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p 〉 5 is an arbitrary odd prime. In this paper, some important propositions on the May spectral sequence are first given, and then a new nontrivial family of homotopy elements is detected in the stable homotopy groups of spheres by the May spectral sequence and the Adams spectral sequence. The new one is of degree p（p - 1）（p^n ＋ sp^2 ＋ sp＋ s） - 7） and is represented by bn-1g0γ^^s in the E2 ^s＋4,＊-term of the Adams spectral sequence, where n≥4 and 3≤s 〈 p - 2. The main theorem obtained in this paper is an obvious generalization of Theorem I in [1].