Stable suspension order of universal phantom maps and some stably indecomposable loop spaces

Abstract

We study a stable suspension order of a universal phantom map out of a space. We prove that it is infinite if $X$ is a non-trivial finite Postnikov space, a classifying space of connected Lie group or a loop space on a connected Lie group with torsion. We also show that the loop spaces on the exceptional Lie groups $E_6$ and $E_7$ are stably indecomposable.