Mod $p$ Decomposition of $H$-spaces of Low Rank

Abstract

Let X be a mod p H -space such that the mod p cohomology is an exterior algebra generated by finitely many generators of degree (2n_1+1, 2n_2+1, \dots, 2n_k+1) with 1 \le n_1 \le n_2 \le \cdots \le n_k . It is known that if n_k-n_1 < p-1 then X decomposes to a product of odd spheres, and if n_k-n_1 < 2 (p-1) then X decomposes to a product of odd spheres and B_n(p) s. In the paper we consider the case of n_k-n_1 < 3 (p-1) , and give a product decomposition of X to irreducible factors.