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Pré-Publication, Document De Travail Année : 2022

Whitehead algorithm for generalized Baumslag-Solitar groups

Résumé

In analogy with the free factors of a free group we define special factors of Generalized Baumslag-Solitar (GBS) groups as non-cyclic subgroups which appear in splittings over infinite cyclic groups. We give an algorithm which, given a GBS group G and an element g ∈ G, decides whether there exists a special factor H < G such that g ∈ H. This algorithm is analogous to an algorithm by Whitehead for free groups. Furthermore we prove that given g ∈ G there exists a unique minimal special factor containing g and give an algorithm which finds it.
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Dates et versions

hal-03741681 , version 1 (01-08-2022)

Identifiants

  • HAL Id : hal-03741681 , version 1

Citer

Chloé Papin. Whitehead algorithm for generalized Baumslag-Solitar groups. 2022. ⟨hal-03741681⟩

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