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

### Yutaka Hemmi

Kochi University, Japan### Hirokazu Nishinobu

Kochi University, Japan

## 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.

## Cite this article

Yutaka Hemmi, Hirokazu Nishinobu, Mod $p$ Decomposition of $H$-spaces of Low Rank. Publ. Res. Inst. Math. Sci. 52 (2016), no. 2, pp. 207–221

DOI 10.4171/PRIMS/178