The problem 10 posed by Tudor Ganea is known as the Ganea conjecture on a c
o-H-space, a space with co-H-structure. Many efforts are devoted to show th
e Ganea conjecture under additional assumptions on the given co-H-structure
. In this paper, we show a homological property of co-H-spaces in a slightl
y general situation. As a corollary, we get the Ganea conjecture for spaces
up to dimension 3.