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Eine Bemerkung zu den Nielsen-Transformationen (1977)

Rosenberger, G. ; Tessun, F.

Springer

Monatshefte für Mathematik 83 (1977), S. 43-52

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ISSN: 1436-5081

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract LetG=H 1* A H 2 a free product with amalgamation with $$H_1 = \left\langle {s_1 ,...,s_m |s_1^{\alpha _1 } = ... = s_m^{\alpha _m } = 1} \right\rangle ,\alpha _i \geqslant 2,m \geqslant 2,$$ 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01303011

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