ON THE PETERSON HIT PROBLEM OF FIVE VARIABLES AND ITS APPLICATIONS TO THE FIFTH SINGER TRANSFER

Abstract

We study the Peterson hit problem of finding a minimal set of genera

tors for the polynomial algebra Pk := F2[x1, x2,...,xk] as a module over

the mod-2 Steenrod algebra, A. In this paper, we explicitly determine a

minimal set of A-generators with k = 5 in degree 15. Using this results

we show that the fifth Singer transfer is an isomorphism in this degree.