THE HIT PROBLEM OF RANK FIVE IN A GENERIC DEGRE

Abstract

Let Ek be an elementary abelian 2-group of rank k and let BEk be the classifying space of Ek. Then, Pk := H∗(BEk) ∼ = F2[x1, x2, . . . , xk], a polynomial algebra in k generators x1, x2, . . . , xk, with the degree of each xi being 1. This algebra is regarded as a module over the mod-2 Steenrod algebra, A. We study the Peterson hit problem of finding a minimal set of generators for A-module Pk. It is an open problem in Algebraic Topology. In this paper, we explicitly determine a minimal set of A-generators for P5 in terms of the admissible monomials for the case of the generic degree m = 2d+2 + 2d+1 - 3 with d ⩾ 6.