A combinatorial approach to the exponents of Moore spaces

Abstract

In this article, we give a combinatorial approach to the exponents of Moore spaces. Our result states that the projection of the $$p^{r+1}$$ -power map of the loop space of the $$(2n+1)$$ -dimensional mod $$p^r$$ Moore space to its atomic piece containing the bottom cell $$T^{2n+1}\{p^r\}$$ is null homotopic for $$n>1$$ , $$p>3$$ and $$r>1$$ . This result strengthens the classical result that $$\Omega T^{2n+1}\{p^r\}$$ has an exponent $$p^{r+1}$$ .