THE HIT PROBLEM OF FIVE VARIABLES IN THE DEGREE THIRTY

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 Pk
in the case k = 5 and the degree 2d+1 − 2 with d 6 4.