# About the proof of Milnor-Novikov theorem about multiplicative generators of (complex) bordism ring

I am trying to understand part of Milnor-Novikov theorem about multiplicative generators of $$MU_* \cong \mathbb Z[x_1, x_2, \dots]$$ using S.Kochman’s “Bordsim, Stable Homotopy and Adams Spectral Sequences”.

Namely, define $$$$\gamma_n = \begin{cases} p\quad&\text{if n = p^t -1 for some prime p and positive integer t}; \\ 1\quad&\text{otherwise}. \end{cases}$$$$

Theorem. (Proposition 4.3.16 in the book) Element $$x_n \in MU_*$$ is a polynomial generator iff $$$$h(x_n) = \pm\gamma_n A_n + \mathrm{decomposable}\in H_*(MU; \mathbb Z).$$$$

I have understood the case $$n \neq p^t-1$$. Can anybody explain to me what happens next? Why does $$h(x_{p^t-1})$$ divisible by $$p$$ and not divisible by and other prime $$p’$$?

It seems that this is because of bidegree of $$h(x_{p^t-1})$$ in ASS, but I cannot understand why.

May be you can suggest me any readable source (different from Stong’s or Ravenel’s books) to find the proof?