Decomposition of $p$-complete $H$-spaces and related problems

Abstract

We work on based CW complexes of finite types. In this paper, we show that each $p$-complete $H$-space can be uniquely decomposed into the product of atomic spaces and that each $p$-complete suspension space can be written as the $p$-completion of the wedge of atomic spaces. We then discuss some related problems on atomic spaces.