The admissible monomial bases for the polynomial algebra of five variables in some types of generic degrees

Abstract

Let Pk be the graded polynomial algebra F2[x1,x2,…,xk] over the prime field of two elements, F2, with the degree of each xi being 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for Pk as a module over the mod-2 Steenrod algebra, A. In this paper, we explicitly determine a minimal set of A-generators for P5 in the case of the generic degrees n=2d+1−1 and n=2d+1−2 for all d⩾6.