Abstract
LetG=H 1* A H 2 a free product with amalgamation with
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.
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Literatur
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Rosenberger, G., Tessun, F. Eine Bemerkung zu den Nielsen-Transformationen. Monatshefte für Mathematik 83, 43–52 (1977). https://doi.org/10.1007/BF01303011
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DOI: https://doi.org/10.1007/BF01303011