In the paper A characteristic property of soluble groups, P. Hall proved that in a finite soluble group, if one has elements $a,b,c,\ldots$ of coprime orders, and you suppose that $abc\ldots=1$, then actually $$a=b=c=\ldots=1$$
He conjecture that this statement is actually equivalent to the property of being soluble.
Is this result already been established? If so, where I can find it?