The secondary periodic elementβ_(p^(2)/p^(2)-1)and its applications  

作　　者：Jianguo Hong Xiangjun Wang Yu Zhang 

机构地区：[1]Science College,Shijiazhuang University,Shijiazhuang 050035,China [2]School of Mathematical Sciences,Nankai University,Tianjin 300071,China [3]Center for Applied Mathematics,Tianjin University,Tianjin 300072,China

出　　处：《Science China Mathematics》2025年第1期207-222,共16页中国科学(数学英文版)

基　　金：supported by National Natural Science Foundation of China(Grant No.12271183);supported by National Natural Science Foundation of China(Grant Nos.12001474 and 12261091)。

摘　　要：Let p≥7 be a prime.We prove thatβ_(p^(2)/p^(2)-1)survives to E_(∞)in the Adams-Novikov spectral sequence.Additionally,using the Thom mapΦ:■,we can see that h0h3 also survives to E_(∞)in the classical Adams spectral sequence.As an application of these results,we prove thatβ^(p)_(p/p)is divisible byβ_(1).

关 键 词：stable homotopy groups of spheres Adams-Novikov spectral sequence in nite descent method 

分 类 号：O15[理学—数学]