We try to investigate whether an element of order in homotopy groups of spheres has a lift to an element of homotopy groups of mod Moore spaces or not. A typical element of the affirmative property is Thomeier's element of . And the Whitehead square of the identity class of is a negative example except for and .
"Lifting to mod Moore spaces." J. Math. Soc. Japan 52 (3) 515 - 533, July, 2000. https://doi.org/10.2969/jmsj/05230515