This interesting paper can be summarized as follows. Let \(F\) be the free product of a finite family \(\mathcal A\) of groups and let \(n=|\mathcal A|\). Let \(m< n\) and let \(R\) be the normal closure in \(F\) of \(m\) elements of \(F\). Let \(R_{\mathcal F}=\bigcap_{K\in \mathcal F}K\), where \(\mathcal F\) is an s-filter, and let \(G=F/R_{\mathcal F}\). (An s-filter \(\mathcal F\) is a family of normal subgroups of \(F\) with certain special properties which we do not elucidate here.) For \(A\in\mathcal A\) let \(\overline A\) denote the image of \(A\) in \(G\) and suppose that for each \(A\in\mathcal A\) with \(\overline A=1\) the Abelianization of \(A\) is not a torsion group. Let \(\mathcal B\) be a family of linked subgroups of \(G\) (where again we do not define what is meant by the term linked) and let \(J=\langle B\mid B\in\mathcal B\rangle\). The main theorem asserts that if, for each \(A\in\mathcal A\) with \(\overline A\neq 1\), the subgroups \(\overline A\) and \(J\) do not generate their free product in \(G\) then \(|\mathcal B|\geq n-m\) and there are \(n-m\) members of \(\mathcal B\) that generate in \(G\) their free product.