Brown-Peterson homology of elementary \(p\)-groups. II
Let \(V=(\mathbb{Z}/p)^n\). In Part I [the first and the second author, Am. J. Math. 107, 427-453 (1985; Zbl 0574.55003)], the associated graded module of a \(\text{BP}_*\)-filtration of \(\text{BP}_*(BV^+)\) was obtained. In the current paper, that result is refined to give the structure of \(\text{BP}_*(BV^+)\) as a graded abelian group. The result is a complicated but explicit formula for the number of summands of each order in each grading. Binomial coefficients play a major role in the final result. A corollary is that there is an additive isomorphism \(\text{BP}_*(BV^+) \approx G_n \otimes Z_{(p)} [v_{n+1}, \dots]\), where \(G_n = \text{BP} \langle n \rangle_*(BV^+)\) is given explicitly. A main tool is an analysis of \(\text{BP}_*(D(n))\), where \(D(n)\) is a spectrum studied previously by Steve Mitchell.
scientific article; zbMATH DE number 681616