Eine Bemerkung zu den Nielsen-Transformationen

LetG=H ₁* _A H ₂ a free product with amalgamation with $$H_1 = leftlangle {s_1 ,...,s_m |s_1^{alpha _1 } = ... = s_m^{alpha _m } = 1} rightrangle ,alpha _i geqslant 2,m geqslant 2,$$ a free product ofm cyclic groups. If we ask for the generation ofG, the following questions are significant: 1) For which α _i andm there is a set {x ₁, ...,x _m } of. generators ofH ₁ withx ₁=(s ₁...s _m )^α, α≥2, and what can we say about α andx ₂, ...,x _m ? 2) for which α _i andm there is a set {x ₁, ...,x _m } of generators ofH ₁ withx ₁=(s ₁...s _m )^α x ₂=h(s ₁...s _m )^β h ^?1, α>0, β>0,h∈H ₁, and what can we say about α, β,h andx ₃, ...,x _m ? In this note we give a complete solution of these questions.