Quotients and subgroups of Baumslag-Solitar groups
classification
🧮 math.GR
math.GT
keywords
groupsbaumslag-solitardetermineembedfinitelygeneratedgivenquotients
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We determine all generalized Baumslag-Solitar groups (finitely generated groups acting on a tree with all stabilizers infinite cyclic) which are quotients of a given Baumslag-Solitar group BS(m,n), and (when BS(m,n) is not Hopfian) which of them also admit BS(m,n) as a quotient. We determine for which values of r,s one may embed BS(r,s) into a given BS(m,n), and we characterize finitely generated groups which embed into some BS(n,n).
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