Detecting the homotopy group of sphere spectrum is an important problem in homotopy theory and the May spectral sequence is the main tool. In the May spectral sequence, some conclusions of the permanent cycles which can be represented by ${\tilde{\gamma }}_{p-1}{h}_0{g}_n$ in the Adams spectral sequence are given with the method of linear algebra, where $p\ge 7$, $n\ge 4$.