We study a stable suspension order of a universal phantom map out of a space. We prove that it is infinite if 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 and are stably indecomposable.
"Stable suspension order of universal phantom maps and some stably indecomposable loop spaces." J. Math. Soc. Japan 59 (1) 97 - 112, January, 2007. https://doi.org/10.2969/jmsj/1180135502