  We study $p$-localizations, where $p$ is an odd prime, of the full
subcategories $S^n$ of stable homotopy category consisting of CW-complexes
having cells in $n$ successive dimensions. Using the technique of triangulated
categories and matrix problems we classify atoms (indecomposable objects) in
$S_p^n$ for $n\le 4(p-1)$ and show that for $n>4(p-1)$ such classification is
wild in the sense of the representation theory.
