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This paper is an English translation of chapter nine of the book "Adamsspectral sequence and stable homotopy groups of spheres" by Jinkun Lin (inChinese)(Sciences Press, Beijing 2007). In this paper, a sequence of newindecomposable families in the stable homotopy groups of spheres such ash_0h_n,h_nb_n,h_0h_nh_m,h_0(h_mb_{n-1}-b_{m-1}h_n) families was detected. Theproof of all the detections was stated in this paper in based on severalpublished papers by the author.

English translation of chapter 9 of the book "Adams spectral sequence  and stable homotopy groups of spheres" by Jijkun Lin (In Chinese)(Sciences  Press, Beijing 2007)