On the hit problem for the polynomial algebra

Abstract

We study the hit problem, set up by F. Peterson, of finding a minimal set of generators for the polynomial algebra Pk:=F2[x1,x2,…,xk] as a module over the mod-2 Steenrod algebra, A. In this Note, we study a minimal set of generators for A-module Pk in some so-called generic degrees and apply these results to explicitly determine the hit problem for k=4.