On the \([p^ k]\)-series in Brown-Peterson homology (Q915195)

Let BP be the Brown-Peterson spectrum at the prime p and let F(x,y) be its (universal p-typical) formal group law. The [n]-series [n]x\(\in BP_*[[x]]\) is defined inductively by \([n]x=F(x,[n-1]x)\) and \([1]x=x\). This series gives the defining relation in the BP-cohomology of the classifying space B\({\mathbb{Z}}/n\) and carries a lot of geometric information. In the present note the author establishes strong divisibility results for the coefficients of \([p^ k]x\). This generalizes results of \textit{D. C. Johnson} [J. Pure Appl. Algebra 48, 263-270 (1987; Zbl 0632.55002)] in the case \(k=1\).